I almost completely disagree with the feedback you've received about the first hand. You're afraid of exactly two hands on the flop; 66 and J6. I think it's very unlikely that a player in the SB (out of position) would re-raise there with 66 and there's a MUCH smaller likelihood that he's holding J6. So you pretty much KNEW that you were leading on the flop.
Sure, you could have raised either the flop or the turn or both in which case all the chips likely would have ended up in the middle (few people are folding KK in this spot even if it's an obvious fold to some of you) --- and the result would have been the same in that case. So I'm not going say you should have handled the flop or turn differently (although you MIGHT have gotten a good player to fold an overpair with a turn shove). I would definitely have raised or shoved the turn, but I'm not at all convinced that a villain with KK will fold there --- and, quite frankly, you WANT that call.
As far as the river goes, AA likely would have played this hand exactly like KK did. If I hadn't already shoved, I would have shoved after being bet into on the river and if the villain has hit is 2-outer, so be it. AA or QQ probably plays this hand exactly the same way and you stack him in both cases. That's just my two cents, though
IMO, all of the prior "analysis" in this hand is biased by knowing the cards that the villain held and the result of the hand. If you had only posted the play up to the river, then posed the river play as a "what would you do" question, I think the responses would be very different.