Hero should reraise PF.
I'd reraise to $4.50, that's standard PF play IMO.
Flop:
As played I'm donk betting the flop. It's difficult for one pair hands to call you on this board and if you hit your flush it'll probably be the best one.
Turn:
As played I really don't know what to do, you played this hand so passively that I have no idea where you stand, I don't see any reason to bet the turn. I'd just check for pot control.
After BTN's raise I'd fold, given his stats he's quite passive and I'd say you're behind quite often.