Danutsinyoeye was right on with all his points.

Hand #1:
It's tough when you flop a good hand with an ace on the board if your opponent doesn't have an ace. The solution is to act afraid of the ace yourself, and hope your opponent tries to push you off. You do this NOT by checking, but by betting the perfect amount. I usually bet 1/2 pot or a little less. Not so little to look like value, but not so much to rep too hard. Just enough to bait him. It's an artform to know exactly what amount is right for what opponent. This is probably the biggest fishing parallel in poker. Checking an ace flop looks suspicious, because repping an ace is such a consistent occurance. You have to rep it to some extent.

Hand #2:
In the second hand what we have is the counterfeit slowplay opportunity. It looks like a good time to slowplay, but it isn't. Slowplay is all about percieved vulnerability. Think about the cards that could beat you on 4th street. Any club, 5, T, bigger two pair. Lots of stuff. What you want out of any situation is to have the right hands paying you. In a situation like this you want an overpair in hand with you.