I don't like to pry. Sometimes guests will offer a lot of info about themselves. In other cases, it's just a quick note.I can't think of any questions that would make us accept or reject someone (other than the ridiculous....ex. "do you intend to trash our house"?)...if anything it's more the questions that they ask that are more of a concern ("I know your listing says you just have the one bed, but is it OK if the rest of the family just sleeps in the car in your driveway?").
When we first started, we asked things like why were they visiting, etc. but found out it doesn't matter/none of our business so we stopped. So far, no problems with any guests.