1) I would cbet this flop and barrel a ton of turns and rivers because his c/c range on this flop has loads of mid/bottom pair and GS or just weak top pair type stuff. I don't think the history is relevant enough to affect my decision here.

As played I probably fold but I wouldn't hate a call. I like a call with AhQh a decent bit better by the way.

Do people think that AQ = A7 here?

Hand 2) Raise>>>fold>>>>>>>>>>>>>>call but I doubt I would think of raising in the moment.