I never ask a question of someone else that I would not want asked of me. I also value privacy so I'd rather that I learned in a natural way instead of a pushy, offensive style. I've met way too many gossips who ask questions that are none of their business, and when they say "I'm just being nosy," that's a guarantee that they won't get an answer.
No, unless the situation warrants imminent danger to that person or someone else such as rape, drug abuse, etc. But in most cases if someone doesn't tell you something, they did that for a reason so you should not push them into sharing personal details about their life.