[Zeldark]

At each individual decision you have no mistakes. When UTG+1 calls and CO caps it for you, you should recognize that this may become a very expensive draw. When it's 2 back to you on the turn you likely should consider that it'll be capped before the street is over. Since they're giving max action already, your implied odds drop to being equal to the pot odds. You may not have the odds anymore to continue if you discount them. There may be fewer Kings and 8s in the deck than you might think.

I would make an evaluation on the turn as to the likelyhood that the 8s would be good, the odds that Kings and/or 8s are in our opponents hands, and if you wanted to invest another 4 BB based on that.

Edit to answer your questions:
I fold on the turn when I think it very well could be 4 bets back to me. The second diamond reduces the value of the draw, as (un)likely as it is.
Also the river is an easy fold. It's 2 bets to you, it'll likely be another 2 after you call. Don't dump another 4BB into this hand. The chances of them both capping every street with something that you beat is even less likely than the odds that you gave of winning that hand.

3-betting to isolate I could see happening if you thought it'd actually get the job done and leave you HU. at 25/50¢ I'm not sure that'd actually work. You also didn't give us any reads on the PFR to further affect this decision. I think the cold-call is fine here.

If it's a 14.5BB pot you're assuming that it gets capped. You are putting in 4 bets out of 30.5. If you're gunning for just kings that's 4 outs and should have about 10.5:1 odds.
30.5:4 = 7.625:1 < 10.5:1. Insufficient odds if you count all 4 Kings as outs. Under your assumptions this is a fold.