I've never had a therapist talk about their own bodies in a sexual way, or describe body parts , or speak in a way that could be construed as encouragement to imagine them naked.

My therapists have asked me what I am feeling in my body at a given moment, but not if I am feeling sexual feelings in particular.

My current t has asked if I want to talk about sex, but that's because it is an issue I am actively working on engaging in therapy right now, not as a question out of the blue.

I think I would have had a difficult time with the vagina waxing remark - my instinct would be to push her on what was going on in her head that that's the analogy she chose. Or I would point and laugh, and feel very uncomfortable about the whole thing later.

The guessing what pet name I would like to be called in bed - oh hell no. Step off, t. Way out of bounds (to me).

Reading your post makes me feel a little uncomfortable and wonder if there is something going on with your t she hasn't addressed in supervision.

Just my .02.