1. I think you gotta call. Prolly up against overpair, set or flush draw in some combo. At least u got the runner runner on top of the usual 2-outter to improve.
2. I has spewed many chips OOP getting attached to what I originally see as an ATS... and by the time you've CBet, you got almost 1/4 of your stack in the middle. In this case, you're hands only good as a bluff by the time you hit the Turn, so calling is totally useless as it will still commit you. So it's shove or fold. I prolly check/fold as I really don't have shit (even if the Ace spikes on the river, according to your range, I'm dead...) and I'm not convinced he folds enough after calling your 3bet, 3/4 flop and then passing on the oppty to pot control and check thru the Turn to make this the kinda spot I wanna toss my stack into.