[W. Deranged]

1. The pre-flop three-bet in my opinion is better here because the cold-caller is quite likely to have a hand that you are significantly ahead of (something like QJ, KQ, AJ and so on). With the likely-donkish cold-caller in between you and the raiser, a three-bet here works nicely because you likely have an equity edge and you can buy position and control of the hand and keep the pot short-handed.

2. Getting over 13-1 at this point I think you need to peel here. BB is not all that likely to have trips already since he called two out of the BB, and often would slowplay such monster flops anyway. Even with some discounting (to like 4.5-5 outs) I think we have clear odds to continue on here. I don't like raising because you don't have that strong a draw, there are not really any outs you can clean up at this point (because of relative position and the fact that you have the second-best possible overcards), and in such a big pot you are unlikely to be able to buy free-cards or to protect a possibly good best hand. You should acknowledge that there is a small portion of the time your hand is still best, but you can't protect it now anyway, and it is better to wait until the turn to reevaluate your holding and the action in front of you before deciding what to do.

3. By the time you get to the turn, the pot will again be pretty big, and you might be getting as much as 9-1 on your turn call. The decision to peel (or even raise) the turn becomes much closer, and you will need to use your reads of the opponents. I think that raising will sometimes be correct if, for example, MP3 folds and you have a read that BB is aggro and might be try to steal a widowed pot, or you think that he is simply on a draw. (You'd be taking a free showdown most of the time in these scenarios).