First of all, I'm not limping with pocket 10's, but for the sake of discussion I'll ignore that.

1) From EP you have to bet this flop to see where you stand. I don't see a 3X BB bet as being particularly strong, just a standard pre-flop bet. It could represent many possible hands. If you check you run the risk of over cards checking behind you and giving them the chance to see a free card. By betting you pressure over cards to fold or pay to chase. Betting the pot should drive out over cards and a re-raise would more than likely indicate an over pair to me. I would probably fold to the re-raiser since he has again shown strength and has position on me or possibly call if the other player calls behind him. With no read though, I'd be more inclined to fold. If the pre-flop raiser just calls my raise on the flop I'd be thinking he has something like AK or two overs with 4 to a flush (assuming there are two suited cards on the board). I don't think an over pair would simply call in this situation, but rather raise. At least he should with another player to act behind him.

Basically I think checking with an overpair in this situation is weak and puts you in a position to be bluffed out of the pot by over cards.

2) Ugh... I don't like simply calling pre-flop in this situation when I have position. Again weak and beside the point.

I am re-raising on the flop and folding to a re-raise. If I call what the hell do I do if another rag comes up and he fires again? Re-raising in this situation also might make hands like JJ or QQ slow down allowing you to take a free card and possibly make a set or allow you to bluff if a scare card like an A comes up.