I'd be checking back the flop, our A high can be good to bluff catch with and by betting I think we fold all worse and own ourselves against PPs.

Turn is an easy bet for value, doesn't make sense to check it back, river I'd be calling as I don't expect regs to be bet/calling with KQ here, not sure about the raise really.

Check back flop is good here, we don't have any backdoors.

Given that we do cbet and spike the K, there is absolutely no reason not to continue betting and to play for stacks.

Usually a call pre flop for me unless I have a read villain is calling wide OOP or stacking off light.

As played I agree with checking flop being the best play. Tough to get value from worse but we can call the turn once villain is induced to take a stab. Once we spike the turn it looks like a standard value bet with a shove on the river.