Yes Ladi is correct. I am not disputing about ritual. I was referring to Student's claim about (Catholic) Melkites not being bound by dogma, as in purgatory and Immaculate Conception. He seems to be confusing Eastern Catholic with Orthodox schismatics.

No, I'm not. My Melkite friend told me this is the way things are in the declaration/agreement of their communion with Rome. Maybe I can ask him to provide a link or reference of the docuмent.
  In it, The Roman Pontiff allows them to remain pretty much autocephalous (self governing) and doesn't impose the Roman Catholic theology or Dogma on them. They also keep their traditional liturgy, etc. Part of the reasoning is that they are what we once were. If orthodox theology is wrong now the Roman church was wrong in the past too. Hence one of their Patriarchs said "We have everything in common with Orthodoxy, and almost nothing with the Romans".
One of the Melkite Metropolitan Bishops has even said that the SSPX and "Resistance" are "instinctively" drawn towards orthodoxy, and already are in in practice to good extent but are essentialy "Orthodox in denial of their real identity".

Yes, I've run into pockets of Eastern Rite Catholics that have a very schismatic orthodox mentality still and almost a contempt for Rome.  Yes, Rome could allow them to remain largely independent ... as they do for many of the Eastern Rites, with regard to Liturgy, Canon Law, discipline, governance.  But no agreement can exempt any Catholic from being required to accept defined dogma with the certainty of faith.

I am not interested in what this "friend" told you.  Provide a docuмent which indicates that Rome has exempted them from accepting DOGMATIC definitions (I'm not talking about Canon Law, liturgy, discipline, etc.).  I don't believe such an exemption exists.  Furthermore, if some Pope did have the audacity to make such an exemption, it's invalid by divine law.  Period.  If any Eastern Catholic, for instance, were to reject the dogma of papal infallibility, he would be a formal heretic and outside the Church.

It should also be noted that Eastern Catholics also recognize Orthodox saints and regularly venerate them in iconography and the liturgy.

I have a friend who left the Roman Rite and is now Melkite Orthodox Catholic. They are only required to acknowledge the Roman Pope as theu did before the Great Schism, they also are allowed by their agreement with Rome to keep everything as is with Orthodoxy. This means that they have the Epiklesia, they are not bound by any of the dogmatic declarations since 1054; Papal Infallability, Imaculate Conception, etc. They also do not share our views on Original sin.

To answer your question in short: They are Autocephalous and maintain the fullness of Orthodoxy, but are in commuunion with Rome according to the ancient understanding of "First amongst equals". The Eastern Rites are still entirely Orthodox in their Traditions.

I don't know why the Romans don't have an Epiklesia, but the Orthodox consider this a grave theological error in our Liturgy. Some will even argue about validity due to it's absence. However, the fact that hosts turn into Blood and Flesh in the Roman Church shows that the Epiklesia is not mainly the vehicle for Transsubstantiation. The same applies to the Orthodox, so while we both see things differently we both have the Most Precious Body and Blood of our Lord and Savior, Jesus Christ.

Regarding your last post, I'm not sure what you mean. Eastern Catholics liturgically commemorate many saints not recognized by the Latins (St. Gregory Palamas, St. Photius the Great, St. Mark of Ephesus) and venerate even more saints in their private devotion such as a host of early modern/modern Russian Orthodox and Greek Orthodox saints. All though this stops short of public commemoration in the liturgy, it is very common to see icons of exclusively Orthodox saints in Eastern Catholic churches.

That's ridiculous. Orthodox saints are canonized the way it was done more or less for most of history, first on a local level then on a wider level. Saints have been declared without undergoing a formal canonization process and without papal involvement even in the West. There are plenty of Orthodox saints, even from the 20th century.

http://www.vaticannews.va/en/pope-francis/mass-casa-santa-marta/2018-02/pope-francis-says-mass-with-melkite-greek-patriarch-.html