Lol; you don't marry Jesus when you become a nun, if that's what you're asking. That's bridal mysticism. It's not literal. You join him in a union by devoting your life to Him, which can be compared to marriage especially in the context of female monasticism. You will almost never see a comparison like that in male monasticism(monkhood). Another example of this kind of mysticism in vocation is when a Priest is ordained he marries the Church (at least in the Latin Rite. Eastern rite priests can get married).
To answer your question: no, you don't have to be a virgin but you must be celibate, and if you're going to be a Catholic nun then yes, you will have to be Catholic. There are Orthodox, Anglican and Lutheran(??) nuns as far as I know of.