Johannes, you might find this excerpt from an article by Ryan Grant instructive:

“None of the cardinals may in any way, or by pretext or reason of any excommunication, suspension, or interdict whatsoever, or of any other ecclesiastical impediment, be excluded from the active and passive election of the supreme pontiff. We hereby suspend such censures solely for the purposes of the said election; at other times they are to remain in vigor” (Vacantis Apostolicae Sedis 34).

Thus you have Pius XII (whom you would assume understands dogmatic theology) and again, whom one would assume understood cuм Ex Apostolatus Officio, teaching us that an excommunicated person can be elected Roman Pontiff. To read into this docuмent distinctions which Pius XII did not put in is to essentially redefine the law contrary to the intentions of the law giver...

This bull was abrogated by the 1917 Code of Canon Law which incorporated these penalties, but never for a pope prior to his election (let alone after). It only says:

Ob tacitam renuntiationem ab ipso jure admissam quaelibet officia vacant ipso facto et sine ulla declaratione, si clericus A fide Catholica publice defecerit. (Can. 188.4)
And:
Omnes a christiana fide apostatae et omnes et singuli haeretici aut schismatici incurrunt ipso facto excommunicationem. (Can. 2314 1.1)

Again, none of these address what to do about the Roman Pontiff. If cuм Ex Apostolatus was still in force, the Code of Canon Law would have taken note of it. The editors of the 1917 Code did not put it in because of the problematic nature of actually enforcing cuм Ex. No dogmatic theology textbook references it, and not one work of ecclesiology from any of the authors you site (Dorsch, etc.) or other recent authors such as Billot, Franzelin, Van Noort, Palmieri or Berry.

As the Sedevacantist journal Sodalitum frankly admits:

“This task [proving an election invalid by the precepts of cuм Ex] however in the current state of affairs, shows itself doubly arduous. To begin with, it is necessary to prove the formal and notorious heresy of the errant one. Failing a (hypothetical) admission of the guilty party, an intervention of the Church and its Magisterium then takes place, in accordance with the words of St. Paul to Titus: “A man that is a heretic, after the first and second admonition, avoid.” What Paul IV perhaps did not foresee—like all the classical writers on the question of the “heretical pope”—was that no authority would arise in such a case to make the admonitions required by scripture and canons.
The second difficulty consists in the current juridical value of the Constitution of Paul VI. The sixth canon of the Code of Canon Law prescribes that what is not taken up again in the 1917 Code should be considered as abrogated, unless the law is evidently by divine right. Now the prescriptions of Paul IV are only partially resumed by the Code (Can. 188.4 and 2314.1) without any mention of the case of the supreme pontiff. Doubt therefore remains about the character of Paul IV’s proclamation—whether it belongs to divine law, and thus is always valid, or to ecclesiastical law.” (Sodalitium, no. 14 pp. 9-10)

Why would the major Sedevacantist journal in Europe not consider it obvious that the bull of Paul IV still applies if it was so evident that it is of divine right and still in force? For the simple reason that it does not.

There is still one more point to consider. What does the 1917 Code of Canon Law say about the loss of office?
“Actus jurisdictionis tam fori externi quam fori interni positus ab excommunicato est illicitus; et, si lata fuerit sententia condemnatoria vel declaratoria etiam invalidus, salvo praescripto can. 2261.3 secus est validus.” (2264)
“An act of jurisdiction carried out by an excommunicated person, whether in the internal or external forum is illicit; and if a condemnatory or declaratory sentence has been pronounced, it is also invalid, without prejudice to Canon 2261.3; otherwise it is valid.”

[Ryan is arguing here against a sedevacantist]:

This is a major problem for your argument. You assert that “a heretic can not conduct his office” to be dogmatic fact. Yet the Church’s law tells us something entirely different: where the Church has failed to declare someone a formal heretic, the powers and uses of his office are still considered valid, though illicit. Thus, if a pope had lapsed into heresy, and he received no correction from the Church (rebuke), his acts would continue to be valid but gravely illicit. Only once the Church had made a judgment of some kind, or better, a rebuke (as in the case of John XXII) could we consider the pope a formal heretic.

Even then, however, there is the question of the right to judge. Either way this is not the case of the last five popes. This is because you refuse (or else are entirely ignorant of canonical distinctions) to admit the difference between a formal heretic—one who has been condemned by the Church and is obstinate—and someone who has not been officially condemned by the Church. If you are going to maintain that ipso facto a heretic is unable to exercise his office, you are going to have to square with the fact that the 1917 Code of Canon law takes the opposite approach. Unless you want to adopt the line from the guy I referenced in a previous refutation who denies that Benedict XV was a true pope, which would then allow you to deny the 1917 Code.

Finally, the Code of Canon Law grants jurisdiction to excommunicated of all classes (vitandi and tolerati) in order to hear confessions if the penitent is in danger of death (Can. 2261). Thus it is inherently possible for the Church to grant jurisdiction to the excommunicated, which means again, it is by no means certain beyond a reasonable doubt that a material heretic could not remain pope, or even a formal one.

Read also this article by Christopher Conlon: https://archive.org/details/TheNon-infallibilityOfcuмExApostolatusOfficio

Pope Paul IV's 1559 Bull, cuм ex Apostolatus officio, is often cited by many Catholics today for its significance in regard to the current crisis of the Church. Some of us have believed this to be an infallible docuмent, and have used that point to add force to our arguments. At other times we have, in thinking the Bull was infallible, declared as heretics those who seem to contradict the Bull. Although this papal bull is certainly significant for our times, we would be entirely mistaken and in error to refer to the Bull as infallible or dogmatic. Some of the greatest Catholic experts on the subject have made it clear that cuм ex Apostolatus officio is not infallible, while the only persons of any standing who have considered it to be infallible have been excommunicated and opposed by the Church. The Catholic experts state that it is beyond certain that the Bull is not infallible, and that it is a ridiculous and enormous blunder to consider it to be such.

Do you believe that heretics are members of the Church? (is this of Divine Law or Ecclesial?)
 
What happens to one's membership for committing the sin of heresy? (same ^^)

Are public heretics presumed guilty until proven innocent? (what does Canon Law say?)

If you have clearly defined Church teaching on these points, then post it. Otherwise, what are you trying to achieve, other than to create confusion and lead people to your sedevacantist views?

"Heretic". What does it mean?

Are we talking about formal heresy which according to scripture and Church law requires admonitions by a superior and pertinacity? Who would give such monitions to the Pope? We don't know. The Church has not settled this question. Let us not set ourselves up as Pope.

"The sin of heresy". Secret heresy is as much a sin as public, manifest (however you might define that term) heresy. Yet St. Robert Bellarmine tells us in his discussion of the "second opinion" that "the foundation of this opinion is that secret heretics are outside the Church, which is false."

The idea that Pope Pius XII was intending by Mystici Corporis to settle such questions is utterly absurd.

As for being guilty until proven innocent, and what you are implying about its impact upon holding office and jurisdiction, where is the evidence that such injustice is part of Church teaching or practice?

This is St Robert Bellarmine's teaching on heretical bishops: "...if the pastor is a bishop, they (the faithful) cannot depose him and put another in his place. For Our Lord and the Apostles only lay down that false prophets are not to be listened to by the people, and not that they depose them. And it is certain that the practice of the Church has always been that heretical bishops be deposed by bishop's councils, or by the Sovereign Pontiff" - De Membris Ecclesiae, Lib I De Clericis, Cap 7 (Opera Omnia, Paris: Vives, 1870, pp 428-429).

And here is some of St Robert's teaching regarding heretical Popes (De Ecclesia, Bk I On Councils, Ch XXI):

"The third condition (my note - the third condition of the Lutherans is that the Roman Pontiff should not summon the Council, nor preside in it...) is unjust, because the Roman Pontiff cannot be deprived of his right to summon Councils and preside over them... unless he were first convicted by the legitimate judgement of a Council and is not the Supreme Pontiff... the supreme prince, as long as he is not declared or judged to have legitimately been deprived of his rule, is always the supreme judge...

"It happens also that the Pope in a Council is not only the judge, but has many colleagues, that is, all the Bishops who, if they could convict him of heresy, they could also judge and depose him even against his will. Therefore, the heretics have nothing: why would they complain if the Roman Pontiff presides at a Council before he were condemned?

"The sixth condition (my note - the sixth condition of the Lutherans required to celebrate a Council is that the Roman Pontiff would absolve all prelates from the oath of fidelity, in which they have been bound) is unjust and impertinent. Unjust, because inferiors ought not be free from the obedience to superior, unless first he were legitimately deposed or declared not to be a superior... it is impertinent, because that oath does not take away the freedom of the Bishops, which is necessary in Councils, for they swear that they will be obedient to the Supreme Pontiff, which is understood as long as he is Pope, and provided he commands these things which, according to God and the sacred canons he can command; but they do not swear that they are not going to say what they think in the Council, or that they are not going to depose him if they were to clearly prove that he is a heretic."

You know what it means in the context I just gave. You can twist yourselves into knots with all the Church law, definitions, and legalisms you want, that isn't my M.O. Heretics don't belong to the Church - every basic catechism teaches this Catholic truth. The sin of heresy "severs one from the Body, by its very nature" no one needed Pope Pius XII to tell us that - Catholics always knew this.

Your M.O., Johannes, as you put it, seems rather to set yourself up as pope and ignore all the Church law and definitions??? Just ignore the entire theological debate and choose the conclusion of your liking and state it as dogma?

It is good to hear a sedevacantist saying that Pope Pius XII only intended in his encyclical MC to tell us what had always been known in this regard. His intention was obviously not to settle the long standing debate about if and how and when the heretic Pope loses office and jurisdiction.

Yet is it not in order to try to prove your sedevacantist theory that you are making such a noise? Pope Francis is a heretic. Heretics are outside the Church. Therefore he cannot be Pope. End of story?

Do you know more than, for example, the great Fr Garrigou-Lagrange?:

Here are a few questions from the Avrille Dominicans' Little Catechism of Sedevacantism:

7. But isn't it true that a pope who becomes a heretic loses the Pontificate?
St. Robert Bellarmine says that a pope who would formally and manifestly become a heretic would lose the pontificate. For that to apply to John Paul II, he would have to be a formal heretic, deliberately refusing the Church's magisterium; and this formal heresy would have to be open and manifest. But if John Paul II often enough makes heretical affirmations or statements that lead to heresy, it cannot easily be shown that he is aware of rejecting any dogma of the Church. And as long as there is no sure proof, then it is more prudent to refrain from judging. This was Archbishop Lefebvre's line of conduct.
8. If a Catholic were convinced that John Paul II is a formal, manifest heretic, should he then conclude that he is no longer pope?
No, he should not, for according to the "common" opinion (Suarez), or even the "more common" opinion (Billuart), theologians think that even an heretical pope can continue to exercise the papacy. For him to lose his jurisdiction, the Catholic bishops (the only judges in matters of faith besides the pope, by Divine will) would have to make a declaration denouncing the pope's heresy.
According to the more common opinion, the Christ, by a particular providence, for the common good and the tranquillity of the Church, continues to give jurisdiction to an even manifestly heretical pontiff until such time as he should be declared a manifest heretic by the Church.³
Now, in so serious a matter, it is not prudent to go against the common opinion.
9. But how can a heretic, who is no longer a member of the Church, be its leader or head?
The Dominican Father Garrigou-Lagrange, basing his reasoning on Billuart, explains in his treatise De Verbo Incarnato (p. 232) that an heretical pope, while no longer a member of the Church, can still be her head. For what is impossible in the case of a physical head is possible (albeit abnormal) for a secondary moral head.
The reason is that, whereas a physical head cannot influence the members without receiving the vital influx of the soul, a moral head, as is the Roman Pontiff, can exercise jurisdiction over the Church even if he does not receive from the soul of the Church any influx of interior faith or charity.
In short, the pope is constituted a member of the Church by his personal faith, which he can lose, but he is head of the visible Church by the jurisdiction and authority which he received, and these can co-­exist with his own heresy.

Well, one thing Cuм Ex clearly does, it gives a layman authority to withdraw obedience, etc.:

"7. Finally, [by this Our Constitution, which is to remain valid in perpetuity, We] also [enact, determine, define and decree]:- that any and all persons who would have been subject to those thus promoted or elevated if they had not previously deviated from the Faith, become heretics, incurred schism or provoked or committed any or all of these, be they members of anysoever of the following categories:

(i) the clergy, secular and religious;

(ii) the laity;

(iii) the Cardinals, even those who shall have taken part in the election of this very Pontiff previously deviating from the Faith or heretical or schismatical, or shall otherwise have consented and vouchsafed obedience to him and shall have venerated him;

(iv) Castellans, Prefects, Captains and Officials, even of Our Beloved City and of the entire Ecclesiastical State, even if they shall be obliged and beholden to those thus promoted or elevated by homage, oath or security; shall be permitted at any time to withdraw with impunity from obedience and devotion to those thus promoted or elevated and to avoid them as warlocks, heathens, publicans, and heresiarchs (the same subject persons, nevertheless, remaining bound by the duty of fidelity and obedience to any future Bishops, Archbishops, Patriarchs, Primates, Cardinals and Roman Pontiff canonically entering)."

For my part, I wouldn't call withdrawing obedience, avoiding as a warlock and heresiarch, etc. as "doing nothing." That's lawful rebellion.

Right.

(musingly) How does one submit to the Roman Pontiff - without which it is impossible to be saved - when they are in rebellion towards the Roman Pontiff?

Here again, you are ignoring the explicit instruction that DR posted from the pope promulgating in his official capacity as supreme head of the Church specifically to the laity, that we are not to obey those superiors who have deviated from the faith, not even the pope.

So first and foremost in the very beginning of cuм ex, the pope makes sure to explain to us that we must contradict a pope who deviates from the faith, then here above he tells us not to obey such a pope (or cardinal etc.)

This papal constitution therefore teaches three important things all Catholics are bound to believe, all of which you deny:
1) Cardinals and popes, contrary to your personal opinion-turned-de fide-doctrine, can indeed deviate from the faith.
2) They remain cardinals and popes who deviate from the faith.
3) We are not to obey them when they deviate from the faith.

^^This is what cuм ex teaches.
NOTE: #1 solves your conundrum:"The pope cannot fall into heresy, but if he does... but the pope cannot fall into heresy, but if he does... and on and on ad infinitum."

To answer your question: "(musingly) How does one submit to the Roman Pontiff - without which it is impossible to be saved - when they are in rebellion towards the Roman Pontiff?"

We should have to continue to obey him as the pope in all those religious matters which fall within the ambit of his authority, UNLESS he should command something which is sinful.

For Catholics, there is absolutely nothing whatsoever complicated about any of this.