The answer to your questions might vary from state to state, but I'm not entirely sure.
When I decided to start testosterone, I had to go and see a gender therapist for four months - although, if you go by the Standards of Care, the therapists will typically make you go for six months. My therapist knew that this was what I wanted, so she was okay with cutting the time down. After therapy, the therapist will write a referral letter to an endo saying that the patient is committed and is ready for HRT (Hormone replacement therapy,) you then take this letter to an endo, they do bloodwork and you're on your way.
Right now, I'm on my stepfather's insurance, so he gets the bill, and he lives in another state, so I don't know what letters he might get,
But I assume that he gets some kind of notification of what the insurance covered.
Sorry that I can't be more help.