It seems you are pushing away a lot at the thought that you may not deserve them or they hurt too much. Don't give back the gifts but definitely talk to your T. about how it all feels. She may adjust her style but I don't think it will be a drastic as your imagining. I think as we go through therapy we need different things at different times. I got mad when my T. called us friends a few months ago but maybe I needed to hear that to increase my lack of trust. I don't know.
You are also saying you aren't capable of having a relationship before it even happens - again pushing away the thought/possibility.
I also used to think about my T. all the time: what is she doing, oh she would like this, think this is funny, etc. It used to really bother me but it has lessened. By that I mean it's not all day or all the time but it's definitely every day. So, I can completely relate. I've told her that I think about her and therapy way too much. She didn't have much of a response - I think she expects it to a degree as part of the processing.