Hand 1: No need to more than double the size of the pot on the flop. A min-raise will give you the information you need to continue on with the hand. Let's say for example he has more than JUST a pair of jacks - You have now given him twice as much money as you should. Let's say for example you have him beat - why would anyone call a bet that is twice the size of the pot with less than TPTK? I know I wouldn't. You turn bet is a bet that I would make if I had a dominating hand and wanted to eliminate any draws. If your opponent was on a draw, he just hit. If you opponent had KJ, I don't see why he would call.

Hand 2: I don't mind the raise on the flop at all. It eliminates odds at drawing (most $.30 bets at this level are donks drawing), and it's not like you overbet here either by betting the pot - you had TPNK. The call on the turn is justifiable as well, you are only investing the same amount as your flop bet to see a showdown. My line if your opponent here had a larger stack would be to see as cheap of a showdown as possible. If your opponent is checking the flop then betting hard afterwards, one pair isn't looing so good. I'd suspect at least a set held here with the all-in.