I really don't like the 3-bet on the BTN unless CO is a really loose calling station fish that has been opening really wide and not folding to 3-bets. If his 3-bet continuing range is really tight, then with KQo you put yourself in a reverse implied odds situation. Having position on the BTN, KQo is a hand you can flat profitably to the CO's opening range; moreover, you are in position to the blinds if either decide to come along.

The flop c-bet is fine, I think a check / call line is fine as well. When CO donks out OTT after you 3-bet and c-bet the flop, I'd be weary of my hand strength. He could have 9x, AK, KQ, KJ, or the flush draw. I think the call is fine given you are getting 3:1 here. OTR, when he jams, you are at best hoping to chop the pot most of the time, so its probably a fold. The tough part is you are getting 3.5:1, so you only have to win 22% of the time to break even here.

I would flat pre. As played turn is definitely close. I might call once & fold the river.

There is a very clear fault in your logic here. On the turn you explicitly state that you think his leading range is "Flush draws and 9x". Then the flush draw completes. So, of the range you have assigned him on the turn you now beat 0 hands, which makes this a trivial fold.

If you beat 0 hands in a persons range, the great odds you are getting to make the call are irrelevant and you should ALWAYS fold.

Plenty of good points already stated... river would be an easy fold.

PF = what aehardin said.

Flop= As played, I would probably bet bigger of flop.

Turn = Although, the price is good I`m folding turn simply because he would almost never lead with worst Kx and neither is it likely he does it with a FD... to be honest it is most likely 9x or AK.