The HAF 922 is wider than a standard atx case. The cpu heatsink will fit. No problem!
Yes, but will it fit in the mobo (ASUS P7P55D EVO)? My RAM is Mushkin PC3-12800 they dont have very tall heatsinks.
The gray colored memory slot closest to the cpu socket is going to be a problem. The memory modules with the extra tall heatspreaders that sort look like a comb usually won't fit in the memory slot closest to the the cpu socket. Tom's Hardware published an article with test results indicating the tall memory heatspreaders don't do very much to improve memory cooling. They're pretty much an advertising gimmick.
If your memory does not have the extra tall heatspreaders then you should be okay. Install the memory before installing the cpu heatsink. It will save a lot of frustration trying to install the memory under the cpu heatsink and fan.