I think it is perfectly fine to ask your therapist how are you today? I would not go into asking any personal questions as the therapy is for you and it is ok to ask about how the therapist thinks you are doing? If you see something in the office I.E. art work etc. that you like certainly make a comment.
If she asks you a question and you just don't have an answer just say so. I would do that as some of the questions just stumped me. My therapist would ask what makes me feel good or feel bad so try not to overthink your sessions.
I thought I was suppose to go home and practice things we talked about and ways to cope with others but she told me all the therapy would take place in her office and I did not have home work. She was teaching me tools to use to help me deal with my depression and feelings of low self-esteem. The biggest thing I learned was to stay in the moment, in the present and not dwell on the past as it is over. The future is not yet here so stay in the moment which is right now.
It is natural to feel anxious re talking to a complete stranger and pour out you feelings but the more you get to know your therapist the easier it gets for you.
Take care my friend and know you are completely normal.