Not a Scooby Doo to be honest.
Raise Pre should indicate some kind of hand so rundown/pair/broadways.
Flop is good for broadway type hands and also can make a set for a lot of the pairs he can have, sets can"t feel too confident on that board though. He could also have two pair although that is not that strong of a hand on that board. AAxx with flush draw is also very possible.
When you bet (pretty big) and he calls I agree that a flush draw is possible. He can also have a set though, I am pretty sure AQxx SHOULD raise does not mean it does of course. He could also have a monster like KKxx or AQxx with the flush draw which is pretty bad for us.
When the board pairs I really think Full houses should be looking to get money in but he could be going for the check/raise. I like your check here.
When he checks the riverI am thinking any FH should have bet, he could still have AQxx or have missed the flush and have AAxx.
I say his range after the river is :-
BUsted Flush
AAxx
AQxx (Less Likely)
Some silly random ten