Hand 2)
I think I check river. I don't think your going to get much value here. A worse Tx might call but your hand is weak, just check it and see what he had to minbet the flop for info.

Hand 3)
raise preflop to about $.12 - $.14. KQ is a good hand to isolate and none of you opps showed strength so try and get it HU. Plus you are in the BB hand will have poor position after so winning it right here isnt a bad result either.
I obviously dont know the villain you were against but you have TPGK and hes betting 1/3 pot. He has presented pretty nice odds. However if this villain has been really passive before, you have to start thinking what he may hold that you beat on the river, given his new found courage to bet at you.
Did you put him on a range at all?
Also, I somewhat disagree with Altruist post on this hand. If its an aggressive player that will bet his draws, then sure reaise flop to charge for draws. If its a weak player, at 2nl, I doubt villain is minraising a straight draw. I dont think you want to ALWAYS reraise in this spot just because thee might be a draw. Most weak players at 2nl try to c/c on the draw, not reraise. Just my thought.