if youre going to bet the flop, bet 1/4 pot or 1/3 pot max. you don't need to protect vs anything, you do want to induce bluffs, you do want to bet this flop getting a cheap price when you have bluffs, and you can get stacks in by river no matter what you bet on flop.
whether or not to bet the flop depends on your opponent. if he is terrible, you should check the flop, because even though when you check this flop you essentially have a hand which will ALWAYS call a turn bet (youre either slowplaying or trying to get to showdown, noone checks this flop with air), villain will still just stupidly assign weakness to your check and try and bet you off your hand. basically, vs guys that bet whenever they get an opportunity, without having a reason why - check the flop.
however, if your opponent is vaguely competent, you should bet really small, as he will see this as weaker (more polarised and therefore including more air), and sometimes go for a small, well-priced check-raise bluff.
in answer to whether or not he can have an ace of course he can, and your line of strong bet/strong bet means you pretty much never get it in good.
*thumb up* Stick likes this ^^^
Check folding for pot control...
Raise slightly more pre
Check back the flop to pot control - there are no bad turn cards on this board for KK so you don't have to protect your hand - if he then checks the turn we bet two streets for value. It's better to get two streets on the turn/river in this spot since we can't get called by worse hands for 3 streets very often anyway and we risk being bluffed off the best hand or bloating the pot to the stage where only better hands can call.
Yes, he can have an ace here, although he has an ace well under half the time.
One thing worth considering is you priced him in to set mine with your tiny preflop 3bet - he raised a limper so he ISNT folding preflop to a reraise at these stakes, make it 1100 maybe? It's not a huge problem though. I'd say the best advice I can give you is check back the flop, then call if he leads into you turn/river (or bet if checked to for value on either street) and if he checks the turn then 2barrel turn/river for value to get paid by a wider range of hands and pot control.