I don't have enough knowledge to comment on hand #2, but in hand #1, the only way he could beat you is if he had AA, which he definitely would have played differently. Am I wrong?

That's pretty close to how I would've played those hands. Except I'd probably have bet a minor amount in the first hand on the flop. Is that a bad idea? Or would a check be better due to the strength of my hand, allowing people to possibly hit something not as strong.