Well it seems like the decision is between call and raise. We are getting 3:1 direct odds and have 11 mostly nut outs and a number of non nut outs that might be good as well. CO kind of has to have something like a set, or maybe two pair + spades or KQ or Q8 to call on the flop. You are not a significant dog to AK + two random cards but against AK + higher hearts you are 2:1 underdog. If CO has just JJJ or TTT he probably won't want to call 3500 more but if he has set and flush draw he might, in which case you risk check / losing the side pot or continuing to put money into the pot with an obviously losing two pair in order to bluff the side on a brick. CO is probably raising the turn himself with AK anyway although BB could obviously have it, but as I said you are only a minor dog to this hand anyway.

I would just call the turn. The river might play out favourably when you hit the nuts and you are getting great odds to proceed. The main pot is kind of protected so you can't really take the pot down now and I'd rather not play a 10k pot oop on the river.

I'd usually check/call this hand on the flop. There are many reasons, but mostly I just don't think this hand fits the betting range very well. Turn cards like this (among many others) show us why.

I don't think CO is always raising the turn with AK (with or without redraws), and our x/r can cost us quite some money when we run into that. I'd just call the turn and lead on spades (except on Ts), K and maybe Q as well. On hearts I'll check/call or check/fold.

I'm not sure but looks like quite lose preflop raise for OOP vs 2 guys, but if you have postflop advantage or they are passive postflop or not 3beting, or BB is very tight is calling, it can be probably OK.

So if you raise that hand preflop, I think this guys are not supper bluffy, and this spot doesn't bluffy for BB range. and CO can have here AK easily. Doesn't looks like you have any FE here. So ch\c + donking good rivers should be the best strategy here.

I think the lead is fine, to hard for anything besides KQ to raise you, and only really Q/J/T turns are bad when you're called. Though I think checking is fine because if it checks around OOP, and after a raise and a flop check the turns that make your hand are less easy to read. Underplaying your equity but disguising your hand isn't a bad result.

On the turn, as played, I think check-calling is the best option. I don't think you'll get many 'fold-fold' results from the check-pot, but with the K+spade outs and the times your boats are good are worth a call.

Call.

Hearts are bad. And so many straights pot is the worst of the 3

Easy call, jam river if improved.

i think its better to call here and jam river.