Hand 1: I don't like checking here on the flop. Although you hold the best hand at the moment, that can change quite easily. Never slow play sets, unless its a set of Aces or Kings, on a rainbow flop with no straight draws.
The goal here is to get as much money in the pot as possible. The more you bet on every street the easier it is to value shove the river.

Hand 2: This is a bad fold. Unless you have a sick read on this guy, this is an easy call in my opinion. You will be surprised how often you will see trip tens, lower flushes, and even overpairs in this situation. Raise turn and call any bet on river.