I prefer to make it at least $0.10 preflop because you have a couple of limpers ahead of you, but the problems here are on the other streets.

Your flop cbet is way too small, standard size is 2/3 to 3/4 of pot. You're letting spade draws see cheap cards here and you aren't building the pot well enough to get value in general. Don't worry about people folding to the cbet, you want that to happen all those times you miss the flop. I take down a huge portion of the flops I see heads-up with my cbet, and a substantial amount of those hands missed the flop. Keep track of which players are bad to cbet against (check-raisers), and otherwise make sure to cbet most of your hands that you raise preflop.

Once the ace hits on the turn you are quite possibly dead. I don't know if this is the absolute correct way to play, but if I have KK I basically shut down as soon as I see an ace, since NL2 players love aces and lots of them will play ace-rag hands all day. Betting $0.10 on the turn is bad for a whole host of reasons. On a non-spade, non-ace turn, you want to again make a bet that's a good-sized fraction of the pot, and on a doom card like this I would just check. No need to throw more money into the pot if you're dead.

Once you check turn, your goal is to see a cheap showdown, since you may still have the best hand. If the opponent checks or makes small bets, good. If he bets big, fold.

Anyway, that's my game plan on a hand like this.