First hand definately use position and call here. I think given that you don't have a whole lot of info to go on, the board isn't extremely scary, and you have the nut redraw, I think it's the best option and not really close. Hard to say what to do on the turn without seeing the card and what your opponent does.

Second hand I have no idea but your really weak half-pot raise preflop sort of puts you in a world of hurt here. My first impression was to call and make your move on a safe turn, and get out of the pot on a nasty turn (king or spade specifically). Very read dependant though as this hand is a lot trickier then the first one...