Sounds like you know what you did wrong. I don't like the min raise on the flop in hand 1. Theres a flush draw out there and possible strait draw too. The guy semi bluff'd a gutshot and the min raise actually almost gave him decent odds to call. With implied odds (63o being a really well disguised hand ) i almost can't blame him for calling the min raise, even though it looked stupid at first. Bet your good hands.

Hand 2 the guy sucks out horrendously, but checking the turn is a big mistake. What hand are you afraid of here? If you're checking because you're scared of KT, JJ, or QQ, you're gonna give up a lot of pots by giving free cards when you only have the 3rd or 4th nuts if you're afraid they're beat. I make it 12$ to see the river.