1) Pot flop. You have tptk, and although you're not loving life right now, you still have to bet for value here in a multiway pot rather than let the draw come in for free. Don't c/c just because the board is gross.
2) Call flop and evaluate turn. Flop is dry so he's going to cbet most of the time regardless of his holding.
3) Wow, how did we get ourselves into this spot? Don't mess around in a 5 way pot, just bet ~$1.5 flop. As played, I would make a $1.5-$2 on the turn. Nobody bet the flop and there are draws out there, it's quite likely you have the best hand right now. Now the river, is villain dependant. The bet sizing leads me to think that he doesn't have a T, since this is a three-way pot, I feel that the villain would be more inclined to bet at least half the pot. But a J would have most likely bet the flop, especially with the draw out there. Some villains might take a stab on the flop with 2nd pair OTB.To me, this feels like a missed draw that didn't want to spend too much bluffing at the pot. Some reads/stats would be nice here.
4) This is fine.