Thank you. I am aware that the Church does not believe the last thing you mentioned. Would you say that it is "dogma" that our Lady died and was then translated to life?
I suppose it depends on how you define "dogma". If "dogma" is just a fancy word for "teaching", then yes. But "dogma" is usually a more technical term specifying a certain category of teaching. The tenets of the Creed, the decrees of the ecumenical councils, etc. are dogma: they are specific affirmations of beliefs which were called into question and defined in such a way as to leave no room for doubt. That our Lady is the Mother of God is dogma: it was called into question, clarified, defined, and alternate opinions were anathematised because, at its heart, that teaching has to do with the person and identity of Christ. I'm not so sure that I'd called the Dormition a "dogma", though. It doesn't seem to have ever risen to that level, seeing as it doesn't directly concern Christ, but was a privilege due to her relation with Christ. It is simply believed by the whole Church, and that belief gives us hope because what is hers now will be ours later. In all likelihood, we probably would not be discussing this teaching in "dogmatic" terms if the Roman Catholics did not define it as such and thus force the issue.
Thank you for your helpful reply. How does one determine what else is necessary? Simply by participating in the liturgy and so on? Some things are said in a liturgical context that do not seem to constitute dogma. For example, the Seven Sleepers of Ephesus are commemorated liturgically at least twice in the calendar. It is said that these "sleepers" miraculously slept for about 200 years in a cave. Presumably, it is not a dogmatic teaching of the Church that this happened, however -- or am I wrong?
What is necessary to believe when joining the Church is the faith of the Church. Basically, if you can assent to the Nicene-Constantinopolitan Creed and to the doctrinal teachings of the ecumenical councils, and generally to everything else the Church believes, that's enough. Now that last bit sounds circular, but faith and the Church are linked. I feel uncomfortable saying "Believe in the Creed and the doctrinal definitions of the ecumenical councils" as if that was the bare minimum. If you think of things in terms of minima, it doesn't make sense. We find that even in the Gospels. The rich young man asks Jesus what must he do, and Jesus lists the commandments. But when he persists in his question because he's done all those things, Jesus tells him to sell everything, give to the poor, and follow him. The bare minimum will only get you so far, but it always points to the "maximum", which is divesting ourselves of what weighs us down and following Christ. We do that, by God's grace, within the Church of believers.
Regarding the Seven Sleepers and their nap, no, it's not a dogmatic teaching. Generally speaking, "phenomena" in the lives of the saints, even if commemorated in our liturgical texts, are not "dogmatic" because they are usually specific to the case of the particular saint. But again, does that mean you don't have to believe it, that you can reject it? It is a tradition regarding seven particular saints which has been received by the Church and celebrated liturgically. I suppose you could study the issue and come up with a guess as to what "really happened" and how that got "hagiographed" into the story we remember today. I don't think that would fundamentally alter our confession of faith, but perhaps it calls into question our notion of faith. Is it so hard for God to cause seven saints to sleep for two centuries? Why does that seem like a mythology but the Resurrection of Christ is considered an undeniable historical fact? If you believe the latter, the former really isn't so bad. It seems rather harmless to believe it, so why call it into question if you're not going to question the weightier matters?
If I am right, then which things that are celebrated liturgically are dogmatic teachings of the Church, and which things are not? How does one discern what one must accept and what is merely theologoumena?
You'll only ever really "get it" within the Church, not by standing outside and trying to use your wits to figure it out. That means you attend the services and pray them. Study the teachings of the Church as expressed in the Creed and in the declarations of the ecumenical councils. Study the Scriptures and how the Fathers interpreted them. Participate in the sacramental life of the Church. The Church holds out certain things as a bare minimum, as I said above, but that's not all she holds out, nor is that the best way of looking at the issue.