[PLAYOFFS]

HAND 1:In the first one, I like checking turn. I don't think he's calling your bet with anything worse than top pair. And if he pushed river I still wouldn't call if turn went check check. I'd call a pot bet there. In summation, I'd try to see a cheap showdown.

HAND 2: By betting that flop I think you MUST call that turn. I hate that situation, but I think in the long run you make more by calling in that specific situation.
If you check the flop, you really give the hand away unless it goes check check. But I think even if they hit top pair they'd check it to trap your vbet on the turn. I don't think I'd play HAND 2 differently.