I think it really depends on the individual and not necessarily the fact that he or she is an American. If you are just getting to know the person, it's probably similar to or even the same in your culture. If the person is a friend, I'm sure you can ask more personal questions. If you are asking about cultural (not personal/private) things, you can ask about anything really. Here are some questions I never ask, even if I know the person well.: Who(m) did you vote for? What score did you get on that test? How much money do you make? Are you in the country legally? Is that your real hair color? And, for some reason, most men won't ask women how old they are or how much they weigh. It's ok to ask the men though. Ha ha. I wouldn't ask questions about that person's personal sex life either, but questions about his/her society's attitudes about sex are fine.

If you are from a different culture, you can ask almost any questions. If it is too embarrassing, they would just accept that you did not know what is expected in their cullture and would forgive you and probably explain to you politely where you went wrong. I have made mistakes many times while travelling and no one seemed too bothered by me.