AKo EP hand, live 1-2 game

[ilya]

Live 1-2 game at a club. I have $400 and make it $10 to go UTG with AKo. UTG+1 and MP call. They both have about $200-$250. They are both poor players who cold-call way too much preflop without giving consideration to things like position and stack sizes. Button ($300) also calls. He's a young guy who seems reasonable. He has some sort of hand, but since he's on the button it could be any pair, any suited connector or one-gapper, many offsuit connectors, some suited two-gappers, etc...you get the idea. SB, a fairly tight player who also seems reasonable, also calls.

Now it's up to BB ($290), and he makes it $40 straight. He's pretty bad, but LAGgy and somewhat unpredictable. I have seen him check-raise all-in with 22 on a 457 Q board after check-calling the flop HU. His opponent was clearly pot-committed to calling the check-raise.

I flat-call his raise. UTG+1 folds but MP calls. Button groans but also calls (he had announced that this would be his last hand). SB folds.

Pot is $180 going to the flop. It's KJT with a flush draw. LAGgy BB instantly pushes for $250. I fold, MP folds, Button goes into the tank and finally folds, claiming he had JT.

So, my questions are:

1, Was calling the preflop raise alright or should I have done something else given my position and the nature of the players behind me?

2, Can I possibly call the flop?

3, Should Button have called with his bottom 2 pair?