You want to adopt better 3-bet sizing. At least pot size, while some people recommend slightly above pot when 3-betting out of position.
Betting 1/2 pot on flop and turn is perfectly fine. I don't know what I would do vs. an overbet shove like what happened here. Hope that helps.

At 2nl zoom you can 3bet bigger oop as they like to see flops. On the turn the call is close as we don't know how many outs you have in all honesty. I think we can safely say you have 9 flush outs (villain likely gets QQ in pre) but if villain has KQ or AQ then your AK outs could be dead. I'd maybe go for 9 flush outs then add on 3 outs to outdraw his TP giving you 24%ish, not quite enough. You could get there if you knew villain was doing this with hands like TJdd . The stats suggest he may be on the aggro side but it is a bit too early to say.

I don't mind the sizing pre. 3 bet sizes have reduced over the years, and this is just the old standard of x3 a 3bb open plus 1bb for being OOP. It's really not a major point, there's arguments for and against smaller/bigger sizings.

Usually I would check call AK on this flop texture but the flush draw makes it a decent cbet with so many good turns.

The double barrel is good with so much equity against Qx. He doesn't need to fold too much to make it profitable. Once he raises though it's a fold. Bluff catching for 75bb+ with ace high won't be good, even with the draws.

The 3 bet size it s ok, if u got stats on him and he doesn't like to fold against 3 bets u can make it higher like 0.24. I like your bets on flop and turn but it s easy fold when he shoves. U got a lot of out s if u put him on a Q, but he might have A Q so it takes some outs from your hand or K Q and it s the same and sometimes he might have 7 6 suited or Q Q. .