Kia,
Some of those questions seem out of line. Others seem to ask for things to help the doctors decide if your wish to change is truly from being a transsexual or if it's some other reason. I do not believe these questions are being asked out of pure malice or even simple curiosity. The doctors have decided they need to know these things to proceed making their decision about your desired changes.
The thing is, if you don't answer the questions, they may very well refuse to help you. If there is somewhere else you can go to begin transition, maybe a private therapist, perhaps that would be a better choice. But if this is your only option, you may have to answer the questions even if they make you feel uncomfortable.
My therapist asked me some very deep and personal questions before he diagnosed me as a transsexual. I answered truthfully and as completely as I could because that was the only way I could be sure he had the information he needed to make this important decision, even though some of them I would never answer to anyone else. I know these answers would never be repeated to anyone so that made me feel a little better too.
Therapy has been uncomfortable for me many times, but I got through so far and I'm on my way to transition, so it worked for me.
hugs & smiles
helen