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1. Yep, custom!
2. Maybe. I don't like throwing away expensive proprietary coolers every time I buy a new GPU. I buy card variants with the cheapest cooler so that I can replace them with the same universal waterblock I use on everything. If a manufacturer sold bare cards and all-in-one...
The primary enthusiast CPU to buy is the Intel i5-4690k. If you want high end performance without sacrificing value, this is the best chip. It is $225 at Amazon.
http://www.amazon.com/dp/B00KPRWB9G/?tag=pcpapi-20
As for motherboards, anything Z87 should be fine. You can find them under...
For sure. But, I think that sort of processing falls under general programming advances, and nVidia is going out of its way to be incompatible with other brands just to pretend like it has something proprietary and special. In other words, it would be as if Intel suddenly decided to call...
PhysX is the name of a marketing gimmick for something that shouldn't have a special name.
Yes, physics simulation is part of the future. PhysX is anti-competition smoke and mirrors.
You'll get a lot better VRM cooling if you put that side fan right up against the video cards near the VRMs.
I'd expect at least another 15C to come off.
EDIT. You might want to remove the GPU shrouds for better targeted VRM cooling from your extra fan.
It will probably work. But maybe not.
I've stored 100% functional power supplies that exploded in a shower of sparks as soon as they were powered on a couple of years later.
tiraides has given you a good build list with suggestions.
The Corsair 200R is small, nice, and cheap, but if you're wanting to sacrifice size and cost for cooling power, consider something like a Fractal Design R4.