It's not rude to ask what a person's religious views are. But you shouldn't press on it too much, I suppose until you got to know them. And you have to remember to be respectful, and not talk down on them.
I don't think it's rude, but ONLY if the person you're asking is someone you know well. Otherwise, I really don't see any reason to ask about stuff like that, unless the other person volunteers the information first.
I don't think it's rude, but dangerous. People get really defensive about religion, I they are not strong enough in their believe the could get mad and leave. That's only if there's a debate of course.