It kind of sounds to me like you've made your decision but are maybe a little unsure. All of your concerns are valid. Your T, in not communicating her contact policy when you asked sounds like she didn't listen to your concern. Her uninvited personal belief comments about private schools are uncalled for, her lack of interest in the way you want to lose weight, and her seeming issues (?) about age are not conducive to your therapy as you note.

I don't know if you have a way to find other therapists, but if you can tell your T that you are looking for a different kind of T, maybe she can at least give you some references, look in the phone book, etc. When interviewing your Ts, it would be a good idea to write your ideas of goals down and ask them how they would handle this. Best of luck! Let us know how it goes.