You limped, making the pot 4000. Villain bet 4000, meaning you only had to call 2400. Not unreasonable.
Flop played standard. Pot 20400.
Turn— you can’t fold to his bet.
So my two questions:
1. If you were going to lead with a fairly speculative hand from early position, would a raise instead of a limp have been a better play? If Villain three-bets you (likely with a super premium hand) you know you are toast and can get away. Not sure your hand plays well out of position if you get called, which is what your limp invites.
2. Is the play on the turn to just call instead of shove? What worse hands would call you?
I don’t know the answer to either of these.