My problem with the "How would you feel...?" is that as someone on the cusp of the Millennial generation, I'd shrug my shoulders. I expect to be googled which is why I google myself periodically and I adjust my privacy setting accordingly.

If I discovered my T had googled me I wouldn't care. Public info is public for anyone who wishes to see it.

The friend request is more problematic, but nothing that can't be brought up in discussion. Technology can be a strange thing and I could see it being accidental. I wouldn't read too much into it until the T had confirmed they'd sent it on purpose. At that point, I'd feel like a boundary was crossed.