I think your sizing is slightly off in spots. I don't mind the min-raising at all, especially with micro stacks after you.
1. Minraising then bombing a really dry board (Q99r) for pot makes no sense. When a reg flats a minraise they obviously have a weak range, you need to "extract value" from that weak range, not scare it off (I realize you had nothing but you know what I'm saying).
2. I'd go 4x SB vs. BB not 3x
3. 3-betting to $4.50 from BB vs. BTN's $1.25 open seems slightly biggish I think you can go $4
4. As JB mentioned, I'd for sure 4-bet smaller in the AQ hand, $10-$11 should be enough, it's pretty important should he do something like flat and you have to play a flop.
AJs hand vs. nit: Not sure how I feel about pre, I think flatting is fine vs. most people but I think I like a squeeze or fold really. Even a 13/8 is going to be slightly wider OTB and you've got dead money in there already.
As played you should VB the river, I mean c'mon, he doesn't have AK.