First thing I want to say is, I think the good news here is that this therapist has anticipated these issues and put their expectations in writing, so you know whether or not you are okay with them from the start. It often happens that therapists don't discuss or contract for such situations and then the clients are caught off guard in very delicate situations by some boundary they were never warned about.

The first question that popped into my mind after reading the 6 month contract was, can it be renewed? I understand you feel the need for long-term security, but this could be a way of ensuring that clients keep coming only if they still need therapy and not just out of habit. I agree that 6 months is too short for depth therapy, but this might be a therapist who only works short term, and this is important to know when you decide whether or not this is the right therapist for you.

Confidentiality outlasts the therapeutic relationship, but it might be different in your country or region, so you should check the laws where you live. On the other hand, just greeting you has more to do with the therapist's tact and your personal boundaries, I think (this may also differ based on specific laws). My suggestion is to let your therapist know that you don't want her to greet you in public, ever, if that is important to you. It is, in my opinion, a very reasonable boundary.

As for erotic transference, again it depends on the therapist's orientation. This sounds to me like a purely behavioral therapist who isn't conerned with long-term or depth therapy, so transference would just hinder that process, unlike in a more psychodynamic therapy which should never try to restrict what you can feel for your therapist as long as you don't act it out.

It sounds to me like you have needs to which this particular therapist isn't willing and / or able to respond. I would suggest to see more therapists before you pick one, if it's at all possible for you.