Micro Stakes Online NL : 25NL AK - OOP in 3bet pot on wet board with TPTK

Full Tilt Poker $0.10/$0.25 No Limit Hold'em - 6 players - View hand 588327
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SB: $25.38
BB: $10.25
UTG: $33.49
MP: $10.35
Hero (CO): $25.00
BTN: $36.85

Pre Flop: ($0.35) Hero is CO with K A
2 folds, Hero raises to $0.75, BTN raises to $3, 2 folds, Hero requests TIME, Hero calls $2.25

Flop: ($6.35) Q T K (2 players)
Hero checks, BTN bets $3, Hero calls $3

Turn: ($12.35) A (2 players)
Hero checks, BTN bets $6, Hero requests TIME

Please review my hand. This is on a Rush table. 25NL Rush plays similar to 5NL-10NL non-Rush in certain ways.

I have these notes on villain, which I'll unabbreviate for you:
3-1-10 - 25NL - Raise 3bb SBvBB(me) w/$21, Pot Cbet 983t before ck/f Kt
3-5-10 - 25NL - Raise 3bb/Call 3bet w/66 SBvBB(me 3bet $2.50 w/AA) w/$27, ck/r 3.1x/Call all-in QJ6r, Kt and Tf arrives and I win. === Set mines OOP vMy slightly big 3Bet BvB. 3Bet to $2.75 over his 3bb SB open next time, value bet him big!

The notes say that I can 3bet him for thin value since he'll call too light, and big; plus that he can cbet big OOP against me on a wet flop with a weak hand/air.

In non-Rush I 4bet preflop here. But in Rush people are more tight-passive, and I don't have stats on this villain yet, so I am unsure what to do here. I often only 4bet KK+ and bluffs in this spot. I plan to call here and check-raise all-in on many flops, or sometimes check-call with a pair. Should I 4bet, and if so, to what size?

I'm behind straights, sets, two pairs, and AA on this flop, but tie AK. I beat some Kings and Aces and Jacks and 98s here though, plus his pairs weaker than mine and air. I'm confused here and am not sure if I should lead, also because I don't know how to handle a raise. I decide to check-evaluate here. Should I bet, if so, what size? As played, should I raise his bet, if so, what size?

The turn is weird for me. Should I bet, if so, what size? As played, should I shove? Thanks, Yojimgari