Tough hands to play HU.

I'm debating myself on the first one. If villain hadn't called 3 cold i.e. just a 2 bet cc, then by all means bet the river. As it is, you probably faced another big ace or a middle to biggish pair, say TT, 77, 66. Maybe a middlish suited connector T9s. Fishy would call 3 with any of those are worse. My guess is that he rolled over a busted draw.

On the second hand, when you checked into the scare card, you were asking for him to take a shot at you. Pot is smallish, so I don't really quarrel with laying down against the 3 flush/4 straight turn card.

Against a LAG I had a good read on, I might bet into him unless I thought he was capable of a bluff raise. If he had something on the turn, he woulda popped and you know you're done. If he doesn't, he's got a similar big ace and you're probably ahead or tied. If you play it that way, you probably need to commit to betting the river UI if he doesn't raise the turn (and river isnt the 4th club or something)...