Hand 1: just like PokerMuzz said

Hand 2: just like Mixchange said

Hand 3: Before you decide to bet the turn, you need to try to assign villain a range of hands that he could be holding (remember, it is not always about the absolute strength of your hand).

I would guess after villains c/c on the flop(plus the fact he didn't reraise PF), he is probably holding:

A-x: 60%
A-Q: 10%
3-3: 10%
A-3: 10%
Some junky hand he may be planning to bluff with: 10%

You are slightly ahead of his range, but consider how he would play each of these hands on the turn.

With a weak ace (not two pair) i would expect him to lead out. Since he neglected to do so i would guess it is less likely he is holding a weak ace.

With a two pair/set hand he is probably looking to c/r the turn or c/c and bet big on the river. He might sometimes lead out but i think it is more likely he would be looking to c/r in this spot.

Basically taking a free card is best not simply because you are drawing to a flush. It is best because hands that you beat will probably fold to a second bet, and hands that beat you will be looking to make a big raise... forcing you to decide if you want to play a big pot with just TPGK.