Hand 1 - Fold Reluctantly
Hand 2 - Bet, representing AK, AQ, hopefully take the pot down. If you check you might aswell say, bet the turn mate, and take the pot away from me. Alternatively, you could check/raise the turn, but thats probably being too clever.
I think hand 2 is the reluctant fold to be honest.
I think in hand 1 his KK is good given the betting that's gone on. The guy in late position has probably taken a stab at it (that's why you play in position afterall and two players have checked to him so he might aswell have a pop at it)
The guy in early posiition could easily have top pair and was hoping someone would bet for him which is what has happened and he now wants to end the hand right now. I think if he had a set he would check-call rather than check raise.
I think your KK is good to go here. ALL IN!!!