Reads would help on both hands.

Hand 1: Kx isn't a very big part of his range, here. I'd probably call the turn bet (it's only 1/3 PSB), and bet any blank on the river. He could play this line with any 5 or two spades, a couple of pp's we beat and Axss that picked up a draw. If the FD/SD don't hit, I think you're well ahead of his range.

Hand 2: Make a note this guy floats. You turned your hand into a bluff, which was it's only value on the river. But why? Honestly, you were probably ahead anyway if he was willing to fold it. I would just check behind here.