Dont think there are much you could have done different in this situation. Would assume its a good call with AQ after he push all inn

(maybe, just maybe you could bet alitle bit on flop, something like 4 just to "smell out" where you are in this hand, since you have another player in this hand with a big stack. And he might have a set 777 or 888 or two pair or something but its very rarely. But think it might be better to bet smaller on the flop to see what happends. Then take it to turn if you get called. The reason for this is that it could save you some money if the player with a big stack has a set, or two pair or something, but then again its very player depended what they would do with those hands, some would reraise JQ Q10 here, some would just call and never reraise unless they have two pair or better. I dont think the bet is to big of a deal, both bets are fine i think.

I think i would never fold AQ against the player who push all inn, unless very very rarely if he is a super tight never reraise unless he has two pair or better kind of player.

So I think you did the right thing in this hand. There are so many hands that you can beat.