Pf is fine. Flop I'd bet $10. Yes, turn raise to ~$20--those donk bets mean someone's trying to price themselves cheaply for their draw, in my experience.

One suggestion I have for changing your thinking about betting alot on marginal hands is to ask yourself, "do I have any reason to not think I'm ahead here?" In this hand, although it's uncomfortable to put so much $$ on TPTK, villain is giving you no reason whatsoever to think you're not ahead.