First things first. You need information on those opponents. Otherwise your decision becomes exponentially harder.
Hand 1: That's a tough position to get away from, and I would have been suspicious on the turn when the overcard came and you were raised. I still probably would have played it the way you did.
Hand 2: It's hard to say here. Again, you need to know your opponents tendencies. I can't stress that enough. If he's a nit it becomes an easy fold. If he's loose than maybe not.