1: I usually fold here unless I'm seeing a trend in his play

2: I don't think it's a big mistake either way. Kinda depends on how much gamble you're feeling.

3: I might actually fold p/f until I have a read on his play. On the turn I think you have to check behind because you're only really getting called by hands that beat you here. However, for image purposes I like this play. (I feel a playstyle that has you betting/raising a lot and not showing fear will increase the likelyhood to get paid off lateron because people will get the impression "he can't have it all the time..")

4. You basically have the worst hand that beats TP.. so assuming he doesn't play TPGK like the nuts, you're either way behind AT/set, or slightly ahead of a big draw like AKhh/AQhh. By his betsize it doesn't look like a simple draw (like 45hh) though, he either wants to put you to the test, or just milk you for more money.
I fold this preflop btw, then you avoid uncomfortable situations like this.