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I don't have much comment on the first hand you posted as I view it as a pretty normal to get it in with this hand unless you both are very deep in the game.

As far as the second hand goes and am surprised that no one has brought it up yet is that you have an effective stack of 2000 and you are tank folding a set on the flop for 90 dollars. You have not been check raised it is your opponent leading out betting. If he actually has KK or 88 why would he lead out instead of check raising to you the original raiser, do you not think it is possible he is raising for information or just to take down the hand there. Also you have an 8 so middle set is unlikely. This looks to me more like a cooler situation by the way of your opponent having K8** with you stacking him with a set. You didn't put any suits out so I am perceiving this as a rainbow board

I just do not understand how you view this as a fold. That is by far the worst of the 3 options. I get not wanting to make a gigantic pot with bottom set on the flop but you are still many choices from getting your stack in.

A flat call and seeing if he continues on the turn is a passive but good option. This leaves you with the ability to raise the turn if he bets out again. Unless he is a pot betting donkey his bet should be 200 or less. So a fairly large raise here will look extremely strong and will usually elicit a call on the turn and a check from him on the river in which case you can decide from there what to do. I say this because if he hits or has a better hand he may be looking at a check raise on the river after the strength you have shown on the turn. If he happens to ship on the turn than it is a matter of your gut feeling on what he has but I think even kings may look to trap a river bet for value.

As far as raising the flop, that is my preference as I put him on K8** and I want to get the pot big before I have to worry about straights or flushes on the turn, and since he is leading out with a bet I want to take control of the hand since I have position on him which should give me one free street if I get called on the flop.