Should I be folding AK on the flop?

Your 3bet is way too small. You are OOP so even against one opponent and 2.5bb open you could 3bet to 0.45 and now you have 2 callers. I would have probably made it at least 0.70$ pre.
Now your villain gets so good price that he might flat your 3bet with 22 and 44. Those are possible but still not very often in his range. On the flop you probably are ahead very often. However I don't see much point in shoving with TPTK. You hold Ah which reduces the amount of opponents draws significantly and if you shove you will get called only by better or a split.

Yes.

PF 3 bet to small.
OTF I don't think it's EV+ to go stacking so deep multiway with TPTK (even more with the small 3B because their range are more wide, 22 - 44 are still there IMO). Since you have the Ah that remove some draws in his range so you're more often behind OTF when called.

Yes, and even more because you are 200bb deep. given spr you need more relative strength

1. This is not a simple 3bet preflop. We are squeezing.
2. We should squeeze bigger as there are 3 players already in the pot.
3. OTF you block the nut FD and I do not think you are ahead after villain's raise. I think folding is ok.

OTF in NL5 I do think he can raise with low FD though. I like calling there.

His raise on flop is quite big so we can fold with just top pair.