Hand 1: I don't see what is wrong with preflop in hand 1. I assumed you called the initial raise because it is right in the middle of the 5/10 rule and you have position. Once there is a reraise, you are getting 3.5 to 1 with enormous implied odds. He reraised from the blinds which normally means JJ+, AK, AQ.
I would raise to 40 on the flop. AK is dropping no matter what you raise. You are losing your stack to QQ no matter what you rasie also. I think 40 is an amount that can be called by AA, KK, and AQ without setting serious warning bells off. There aren't really any draws you should be worried about.

If called, I would bet about 3/5 pot on turn.

Hand 2: I would probably play it the same way, but I don't know what is optimal. I guess checking the flop is a possible line, but that could create some really tough decisions when 77 or something tries to take the pot away from you.