I could be wrong about vows of celibacy, but I was pretty sure they have at least commitments to celebacy. Here's a story that backs up what I've said: https://archive.ph/ehobt

You are right. You are only eligible to be in a seminary if you're not married (ok exceptions exist, but then you cannot be a priest) and so long as you are not married you are not supposed to have sex.

It's only in the Latin rite can you not be a priest when married; we had a Byzantine Catholic priest at our (Latin rite) church who was married, and the Byzantine Catholics are in full communion with Rome. Priests, however, may not marry so they need to have been married before taking their vows.

There is technically an exception with Catholics of Byzantine Rite, where married men can become priests and most priests are, in fact, married.

Unless they edited their comment, it reads "many gay priests" (not "most") which is vague and can mean any number, small or large. Though a source would be helpful still.