My main problem with this hand is that I decided to call the flop raise (although it is a min raise). The T does not complete any draws and villain's range is still very polarized--so if I'm calling the F, shouldn't I be auto-calling this T?

I think when villain sees us bet/call the F, he is almost always certain we have TP+ or a strong draw, so I can't imagine he would take this line with a bluff, especially when he can take the free card on the turn. Even though it's bad too assume, I feel pretty confident that villain has a set here or at least J10 (note that we also block KQ).

Winning Poker Network (Yatahay) - 400/800 NL - Holdem - 8 players
Hand converted by PokerTracker 4

MP+1: 6.25 BB
CO: 40.76 BB (VPIP: 36.67, PFR: 26.92, 3Bet Preflop: 14.29, Hands: 30)
BTN: 20.16 BB (VPIP: 40.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 5)
SB: 26.36 BB (VPIP: 40.63, PFR: 19.05, 3Bet Preflop: 0.00, Hands: 64)
BB: 25.81 BB (VPIP: 30.00, PFR: 20.00, 3Bet Preflop: 66.67, Hands: 10)
UTG: 24.22 BB (VPIP: 26.67, PFR: 26.67, 3Bet Preflop: 75.00, Hands: 15)
Hero (UTG+1): 37.13 BB
MP: 48.21 BB (VPIP: 33.33, PFR: 26.67, 3Bet Preflop: 0.00, Hands: 15)

8 players post ante of 0 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.25 BB) Hero has A K

fold, Hero raises to 2.2 BB, fold, fold, CO calls 2.2 BB, fold, fold, BB calls 1.2 BB

Flop: (7.85 BB, 3 players) K 9 8
BB checks, Hero bets 3.97 BB, CO raises to 7.95 BB, fold, Hero calls 3.97 BB

Turn: (23.75 BB, 2 players) 6
Hero checks, CO bets 30.52 BB and is all-in, fold

CO wins 23.75 BB

I'd probably just jam the flop since it's a pretty wet board. Lots of turns will be tricky to play OOP and could slow down the action if he has a worse one pair hand. As played, call turn for sure. He can min raise the flop here with a lot of different hands. Sure, on the turn he can show up with sets and two pair, but he can also show up with worse Kx, potentially some hands like TT-QQ or worse, and a bunch of different draws.