BET/FOLD? CHECK/CALL? CHECK/FOLD?

I would x OTF. Villains have straights and bunch of KJ. We have TP + GS, we don´t want to face a raise, so I think it fits into xc range just fine. Also if betting, I think u should go smaller. I think T is fine. OTR I would decide based on the sizing. I don´t see villain bluffing there often enough, so we can overfold imo. I think he´d have to turn something like KJ into a bluff. Ppl don´t do that :).

I do not think he often has JJ here so probably check call OTR and just like Mozzek said I would rather go check call OTF because you play OOP and your hand is not that good on the flop if he 3bets

I'd check the flop.
That's a flop that supposely connects a lot with your UTG opening range, so a cbet is completely standard. If the villain didn't catch a piece of this flop, you won't get any action from him, which doesn't allow you to extract value from your good hand.
OTF check-call I think is the best play overall. Check-raise is better than cbetting because you get some more of his money in the pot, but the effect is pratically the same: make him fold if doesn't have nothing; make him continue with hands that beat you.

You get the nuts on the turn so it's time to start building the pot. Besides, it's likely he has caught something on it too, so just go for value here with something around 2/3 to 3/4 of the pot.

River is nasty. I can't see any reason for betting here.
He called your turn bet and now the board pairs... There's not much you beat here he'd call with I think.
- AK, KK, AA, QQ are unlikely because of the pre-flop action.
- JJ, QJ, QK are now full-houses and consistent with how the action unfold up to this point.
- You block TT, AQ, AJ, AT.
- AT, TT, QT are the only hands you split the pot with. The rest you lose to. But you block this hands.

So OTR I'd just check-call his bet if it's not too big.

Check the floop seems fine. Nearly all Ax hands in his range beat you.
xc river.