I don't think there's anything wrong with asking those questions - they don't seem overly personal. Just be prepared for your T to ask why it's important for you to know. And, you T may choose not to answer the questions.

I have asked my T basic personal questions - are you married, do you have kids, etc. Also, random personal stuff has come up during the course of our sessions. For example, my T once said something that reminded me so much of a friend of mine that I asked T where she grew up, because it was a very "regional" thing for her to say. She easily shared that with me, as it made sense in the context of the conversation.