hand 1

I checked the flop to see what would develop, and I was willing to let the hand go to any kind of action. I figured if I bet out and got called, I would be in a bad place on the turn either bet/folding or check/folding. I'm guessing he either had 77, 88, JJ or T9 and put me on AA/AK hoping I would pay him off.
You're going to check TPTK on a very dangerous flop, but lead out with it on the turn when 4 people acting after you have had the chance to see another card? If you're going to bet this hand then bet it on the flop. You get much more information betting than you do checking, and you also give yourself a better chance to win.

hand 2 - given your reads, i think you were correct in folding

hand 3 - You represented trips on the turn and he still called you. Did you think he would then fold on the river to a bet that wasn't much larger? I check/call or check/fold here.