If it helps any, I have been improving since January (after 6 years of crippling depression) None of my Ts has suggested we terminate. In fact I am going to initiate termination with one because I actually want to! In my experience, ts are delighted to know that clients are improving but they know very well that the start of improvement doesn't mean that clients are done. I would talk to t about this in general terms if necessary, asking who initiates termination, is there a process, how you know it's time.
As far as FB, there is a way to keep all your stuff private. IMO anyone who has a FB is putting the info out there for the world to see. In the olden days of phone books, a person could opt to have an unlisted number. If they didn't do that, then they were making their phone number and address available to whoever cared to look. I think FB is the same. I do not think that googling or looking up on FB needs to be disclosed nor do I think ts should get upset about it. That said, if you feel bad about it, stop doing it and plan to tell t that you did it in a year so they know that you are not going to start stalking.