Your T's style sounds completely different to mine but I share many of the same feelings. However. like Stopdog says above, looking for info on your T on the internet isn't stalking. It's not as if you're tracking her movements or hacking into her text or emails, you're just trying to find info which is freely available online and which she has some control over. That isn't an issue in my book but I do understand the feelings about it.

Your T sounds at the extreme end of 'blank slate' to the point she behaves more like a robot than a person in the room with you. You don't have to be okay with this approach if it doesn't suit your needs. Humanistic therapists tend to be themselves more in the room due to their belief in being genuine with the client, but it very much depends on the individual therapist above all.

As for feeling jealous of T's family, yes I feel like this a lot. I see a private T at her house and so her personal life is more obvious to me than when I was seeing a T at an agency. In some ways I like this better but this may be because of how my T is - she's very flexible, open, genuine and warm. I do see her in a separate room to her family life but I have seen family members on occasions and I see her home environment. This brings up painful feelings of jealousy and longing to be part of her life in that way. What helps me is trying to be open with T about these feelings. I tell her that I wish I could have more with her, that I wish I could live with her 24/7 and be part of her life. She is always understanding and empathetic. Somehow being able to voice these feelings helps them to settle a little more inside so they don't overwhelm me so much. I think it's because she always accepts them (and therefore me) without being shocked or getting defensive, or making me feel shamed for having these feelings. She doesn't tell me I have to move on from them or see things differently, She just accepts me where I am. This has helped me to let go, little by little, of the intense needs.

Unfortunately, given your description of your T, it seems she might not respond as warmly as my T but this doesn't mean you can't express these feelings to her and see how she reacts. I understand there are limits with who you can see so the fear is going to be strong around doing this but if she's a good T she will understand how you feel, and if she isn't she isn't going to be much help anyway. I really hope you can work with her.