Hi,
it is correct that you will need a German health insurance if you want to study here. The insurance will pay a psychologist. As soon as you have your insurance card you can go to a psychologist. You get five appointments without any need for talking to your insurance. After the five appointments the psychologist will have to write a proposal for a psychotherapy, but he/she will do that for you.
The hormones, mastectomy, etc. is also payed by the insurance if certain conditions are fulfilled. That is that you have to be seeing your therapist for a while and you do the Real-Life Test, i.e., have to live "as a man" for some time. Then you can write a proposal for the treatment.