I think that since therapy is such a one-sided relationship, it is somewhat natural to wonder about your t.

While I would never outright ask my t about her issues, I don't think asking completely crosses the line. It may prompt a discussion about therapy being focused on you and what the boundaries of the therapy relationship are. If you ask, you have to be ready for your t to say she is not going to answer your questions for the reasons others have stated above. However, pursuing the issue after your t makes it clear she is not going to answer would be crossing the line.