Are the FSSP priests at the church I attend actually priests or are they laymen. The bishop who ordained them was consecrated under the new rite. If that rite is invalid, then he cannot actually ordain priests. 

The simple answer is "it depends".  Lots of investigation is required on who consecrated who, and who ordained who.  Doubt is not an easy thing to overcome.  Personally, i'm well within my catholic rights to assume they aren't ordained, until such doubt is removed.  I treat them with respect all the same, but still, when the Church reaches a saner day, and if I was one of these FSSP guys, I'd run to be conditionally ordained.  Not only to appease my conscience but, more importantly, to cast aside all doubts in the minds of the faithful, so that the devil can't use this as confusion.

ByzCat, I think it's interesting when non-sedevacantists come up with these questions rather than the sedevacantists.  

Since someone brought up the possibility that the doubt could be based on circuмstances, maybe the question to ask them would be (Rather than speaking of this or that priest or bishop ordained/consecrated in the New Rite):

If Bergoglio or Ratzinger , as "pope" , were to offer the Sacrifice of the Mass (ie. the Traditional Latin Mass) would they assist at that mass?  If not, why not?

TBH I'm more inclined to agree with the R + R on most things.  I don't necessarily feel obligated to agree with everything in papal encyclicals, though obviously we'd normatively give them more deference than we do now.  But like, I'm not terribly bothered by the idea that Popes could teach serious errors in their non infallible capacity.  As a non Sedevacantist, I come to this conclusion the same exact way the Sedevacantist does (That Francis has taught certain things that are seriously wrong).  I don't feel the need to take the "therefore he isn't Pope" extra step that sedes do.  That being said, for a true Pope to invalidate the holy orders of the entire Church seems a step too far to me.  That's not just him teaching stuff that's wrong, that's him basically making the visible Church not the visble Church.  For whatever good that is, that seems to violate my common sense.

Now maybe there are abuses made by some bishops in the new rites of ordination/consecration that make them invalid ,but provided they are done "by the book" I don't see how they can possibly be invalid if the conciliar popes are true popes.  I think Salza and Siscoe's arguments there are pretty convincing as well.

Yes, I'd attend a TLM offered by Francis or Benedict.  Actually I might not, but the reason why if I didn't would be because the kind of crowd that would be gathered around a papal mass would likely be overwhelmingly stressful to me as an autistic person.  But like leaving that aside, yeah on principle I wouldn't object to it.  As much as they aren't good popes, I believe they're real popes, which means I believe they're real bishops, which means I could assist at a TLM. 

I realize most people here would disagree with this, based on the assumptions #1: That Francis/Benedict are doubtfully consecrated.  #2: Scandal of some kind.  #3: That attendance at the indult is an implicit acceptance of the Novus Ordo.

I currently think #1 is false... I respect it but I don't agree with it.  I'm theoretically persuadable but I think the burden of proof is majorly on the side that makes that argument.  Our default assumption should be that the Church didn't invalidate her orders.  #2 would need to be defined for me.  I don't really accept #3 either.  Like even if the Pope said somewhere that that's the case, I still never agreed to that.  

When Fr. Calderon declares the new rite is “probably valid,” he is simultaneously saying it is doubtful, yes.

I've not read what Fr Calderon said, so trying to understand.  It seems to me that each sacrament that has changed would have different degrees of doubt, based on degree of change.  So which sacrament was Fr Calderon saying was "probably valid"? 

I've not read what Fr Calderon said, so trying to understand.  It seems to me that each sacrament that has changed would have different degrees of doubt, based on degree of change.  So which sacrament was Fr Calderon saying was "probably valid"?

The new rite of episcopal consecration.

He was defending it.

But of course, a sacrament only “probably valid” is therefore doubtful (ie., because anything short of “certainly valid” simultaneously admits to being doubtful).

Now maybe there are abuses made by some bishops in the new rites of ordination/consecration that make them invalid, but provided they are done "by the book" I don't see how they can possibly be invalid if the conciliar popes are true popes.  I think Salza and Siscoe's arguments there are pretty convincing as well.

Many different Trads from different groups have come to the same conclusion that the changes are problematic. 
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That being said, for a true Pope to invalidate the holy orders of the entire Church seems a step too far to me. 

Ahh, but not all holy orders of the entire Church are invalidated, only those of the new rite.  The old rite still exists, thus so does the Church.  Your comment of "a step too far" is understandable, but also a human reaction.  Were not the Apostles scandalized when Our Lord was captured, scourged and crucified?  Didn't they think that God had gone "one step too far" in allowing Himself to suffer?  In the same way, as the Church is currently going through Her own passion, then how can we say what is "too far" and what isn't?  God's ways are not our ways. 
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That's not just him teaching stuff that's wrong, that's him basically making the visible Church not the visble Church.  For whatever good that is, that seems to violate my common sense.

But the visible Church is still visible, as long as there are Traditional Bishops, priests and laity.  It is not a doctrine/requirement for the pope/cardinals/priests to ALL hold the Faith.  The Arian heresy (as well as other times) prove that a general falling away from the Faith, mixed with invalid orders/sacraments is not out of the question.  Remember it was "St Athanasius against the world" while the world "groaned under the heresy of Arianism".  Our times, while worse, are very similar to Arianism.
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I realize most people here would disagree with this, based on the assumptions #1: That Francis/Benedict are doubtfully consecrated.  #2: Scandal of some kind.  #3: That attendance at the indult is an implicit acceptance of the Novus Ordo.

I currently think #1 is false... I respect it but I don't agree with it.  I'm theoretically persuadable but I think the burden of proof is majorly on the side that makes that argument.  Our default assumption should be that the Church didn't invalidate her orders.  #2 would need to be defined for me.  I don't really accept #3 either.  Like even if the Pope said somewhere that that's the case, I still never agreed to that. 

#1.  The episcopal consecration is doubtful.  That's a fact.
#3.  Both the Ecclesia Dei docuмent of the 80s and +Benedict's "motu" of 2007 specifically mention that attendance at an "under Rome" latin mass is acceptance of the new mass.  It's the law and it's public.  Your ignorance of this fact doesn't change the reality.

My comments, in red, on the Billot article.  I read it differently than you.
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Finally, whatever you still think about the possibility or impossibility of the aforementioned hypothesis [of a Pope falling into heresy], at least one point must be considered absolutely incontrovertible and placed firmly above any doubt whatever: the adhesion of the universal Church will be always, in itself, an infallible sign of the legitimacy of a determined Pontiff  (determined pontiff = he's speaking of an election), and therefore also of the existence of all the conditions required for legitimacy itself  (he's saying that universal acceptance means the pope-elect is ABLE to be pope.  He's saying they have fulfilled the conditions TO BE ELECTED.  Since one can be elected without being a bishop, this acceptance does not provide the episcopal faculties, it only says the person has the POTENTIAL to be a bishop, with no impediments.).

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It is not necessary to look far for the proof of this, but we find it immediately in the promise and the infallible providence of Christ: ‘The gates of hell shall not prevail against it,’ and ‘Behold I shall be with you all days.’ For the adhesion of the Church to a false Pontiff would be the same as its adhesion to a false rule of faith,[2] seeing that the Pope is the living rule of faith which the Church must follow and which in fact she always follows. As will become even more clear by what we shall say later, God can permit that at times a vacancy in the Apostolic See be prolonged for a long time. He can also permit that doubt arise about the legitimacy of this or that election. He cannot however permit that the whole Church accept as Pontiff him who is not so truly and legitimately.

"Therefore, from the moment in which the Pope is accepted by the Church and united to her as the head to the body, it is no longer permitted to raise doubts about a possible vice of election or a possible lack of any condition whatsoever necessary for legitimacy. For the aforementioned adhesion of the Church heals in the root all fault in the election and proves infallibly the existence of all the required conditions.”[3]

(Since it is not a condition to be a bishop to be elected pope, then the legitimacy of an election does not depend on this fact.  So, it is not a FAULT of the pope-elect.  Therefore, Billot's comment of a "healing" does not apply to the lack of episcopacy.  I think he's talking about the doubts related to if one was ineligible to be elected (i.e. questionable orthodoxy in the past, age requirements, possible voting scandals, etc).)

Yes, we read it differently, because when I see Billot speaking of “all the conditions required for legitimacy,” I note that election is only one of them.  Therefore i conclude he is speaking about more than just election when discussing legitimacy.

In other words, the quote isn’t primarily about elections, but legitimacy of the one so elected.

Yes. If anyone still doubts the validity of the new rite after Pope Benedict XVI was manifestly universally accepted (and therefore known to have become Bishop of Rome) in Rome, he ipso facto commits an objective mortal sin and denies two dogmatic facts (1) that Pope Benedict XVI, in 2005, was Sovereign Pontiff of the Universal Church. (2) that Pope Benedict XVI, in 2005, was the reigning Bishop of Rome, and therefore known with infallible certainty to be a valid Bishop. In other words, just as the fact alone of Universal Acceptance proves infallibly the existence of all the conditions required, and makes continued doubt regarding his person as Pope sinful and illicit, it also makes continued doubt of the validity of the rite in which he was consecrated Bishop likewise sinful and illicit. In 2007, there was an excellent study by Fr. Pierre Marie, proving from two Eastern rites, the Coptic and the West Syrian, that the NREC is surely valid.

Some of the careless people here don't say that they make an absolute mockery of the Roman Catholic religion by professing and teaching as their own self-invented dogmatic fact that rites the Roman Church has used for 50+years are invalid. Get ready to see mor people running to the Eastern Orthodox Churches, then, as we've already seen, as you yourself undermine the Roman Church so badly.

This was a serious conversation before you joined it.

But he finishes the sentence by using the term "determined pontiff" which can only refer to a pope-elect.  The entire focus of the article is about the election.  He doesn't even mention the words "ordination" or "episcopacy".
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Secondly, when he uses the term "legitimacy" he's speaking of a valid election.  What is required for a legimate papal election?  (paraphrasing and generalizing here)...An unmarried male, of the proper age, with no impediments to being (in the future) ordained and consecrated, who was properly elected by the Church.
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The secondary step of being ordained/consecrated is part of the VALIDITY of being pope, but not the LEGITIMACY (which only deals with the election and the Church's role in choosing the candidate).  Properly speaking, we talk of sacraments being valid, not legitimate.  In theory, a layman could be legitimately elected, and die the next day before being made a priest/bishop.  He would be the legitimate pope-elect, but such acceptance by the Church cannot supply the lack of sacramental character.

Disagree:

He only mentions elections once, but constantly refers to legitimacy and conditions of legitimacy;

“Determined pontiff” does not refer to an elected man, but to one who intends to exercise his jurisdiction;

The entire substance of the quote pertains not to whether an election was valid, but to whether the legitimacy of a pope can be held doubtful for any reason once his papacy has been ratified by the universal Church.