First hand you have to call. He's not raising the turn on a flush draw. If he was gonna raise that draw, he would have done so on the flop. CALL

Second hand is a tough one. Maybe a good laydown. Maybe not. You have to consider the psychology of your opponent. Why did he just call the flop bet? You have to ask yourself why he went all in when you checked if he just turned trip kings. The thing about it is at these low stakes, people play weird. At a higher stake someone with top pair raises you for info on the flop when bet into. At a higher stake someone doesn't go all in against shown preflop strength when they turn a 3rd king. They bet for value and know you'll ride along.

All things considered, maybe it's best to pick a better spot since reads are tough against bad players. I don't think he has the king however. I think he bluffed you out of the pot when you showed him it scared you. The best thing to do on that turn is to bet the same amount as the flop if not a tiny bit more. That way you know a raise is actually a king. Get in the habit of staying in control of a hand until someone strongly suggests otherwise. Your check was VERY weak on that turn.