Passively played AK (reasoning within)

MP ($36.84)
Hero (Button) ($25)
SB ($9.57)
BB ($20.35)
UTG ($33.52)

Preflop: Hero is Button with A, K
1 fold, MP bets $0.75, Hero calls $0.75, 1 fold, BB raises to $3, 1 fold, Hero calls $2.25

Flop: ($6.85) 4, 2, Q (2 players)
BB checks, Hero bets $3.50, BB calls $3.50

Turn: ($13.85) A (2 players)
BB checks ????

OK, this hand is oddly played. I played it very passively preflop, which I'm not sure about, but at the time it seemed reasonable so I explain my reasoning below.

I flatted pf because the UTG+1 raiser folds a lot to 3bets. I didn't want to push out a dominated hand, and 3betting his EP open looks pretty strong. Is this a mistake to flat here?

Once it gets 3bet by the BB who is 13/8 with a 5% 3bet, I just flat again because I'd prefer to see a flop with AK than jam it like a lot of people would. Is this a mistake?

Further to that, my thoughts on jamming over him here are mixed. On the one hand, his 3bet range is very tight, and a lot of it is made hands, so I'd prefer to see a flop and go from there. On the other hand, he is a nit and 5% still includes quite a few made hands (TT/JJ maybe he'll fold QQ) that he will fold if I jam, that I would be flipping with if he calls, so it's OK either way - if he folds it's money in the bank, if he calls I'm nearly always no worse than flipping.

I'm not sure how I feel about jamming here after flatting the first raise too - on the one hand it looks kind of wierd, and may induce him to call, which negates the point of jamming - to end the hand there against a number of hands which actually are marginal favourites to win, on the other hand flatting then jamming could look really strong (if he's also thinking "what would I do with AA/KK if UTG+1 opened and he folds to 3bets a lot?"), and induce him to fold something as strong as QQ. What do you think?

On balance, my own feelings, aside from results, are that I should have jammed over the 3bet. It may look wierd, but so what. I'd have saved myself a tricky spot postflop, and anyway I'm often going to flop fuck-all as I did here, and it'd be preferable to take it down preflop the 2/3 of the time that I flop nothing.

I'm also very interested in critique of the postflop action. I'm happy to hear comments to the tune of "you fucked this up preflop", since I maybe should never have ended up there in the first place, but once I did, I had to deal with the situation as it presented itself, so I think there's something to be learned from that, even if I should never have got myself there anyway.

Postflop, do you donk this once it's checked to you, and once I get called on the flop, what are you doing when the Ace turns?