I am not a fan of the Corsair RAM, but if you have to get Corsair in able to get low profile RAM so it works with the processor cooler then that is what you have to do.
I don't have a Hyper 212 nor have I ever so I can't really advise about how it would affect the RAM. Lots of people with coolers end up getting low profile RAM, though, maybe to be on the safe side or maybe because it is required.
If the case will fit the board and one card then it should have no problems fitting a second card.
If you get the regular gigabyte atx motherboard and the xfx 850w that I chose, you should have no problems fitting and powering 2x 560TIs and you should have no problems fitting the whole thing in the HAF 922.
If you change any of those parts, I would have to evaluate again.