villain laggy over a tiny sample but no further reads

First question about pre as I'm not that experienced about playing deep. AAK looks like a hand I wanna 3bet in any color 100BBs deep but does this also hold for lets say AAKx no suits 250 BBs deep OOP?

Here I felt like this is close to a c/f even but felt like a gutter, an overpair with some outs to his 2p and a 2nd nut flush blocker is good enough to still make the call.

About my turn & river player I'm really not sure. OTT I felt like my hand is barely good enough to call again because I now beat his QJ and he might still barrel a whole lot of draws but playing the river will be very difficult if he barrels off intelligently. I also wasn't sure about what to do on runouts like these. Do I have enough SDvalue to try seeing a free one or does it make more sense to use my blocker and lead into him to fold out 8x and maybe T9? I don't think I can c/r given that a lot of boats are possible so I'm kinda forced to c/f once I decided to check the river.
Really curious about this spot