Read the Guide to Display Cables, Adapters, and Converters. I'm pretty sure it can't as it can only use single-link DVI connection from what the guide says.
http://au.pcpartpicker.com/p/PTFdNG
This should be good.
Just threw in a case that looked decent. Didn't realise that the video card wouldn't fit properly, sorry. The case really doesn't matter that much, as long as everything fits.
If my calculations are correct 3 1080p monitors are about 6 million pixels and 4K is about 8 million. So 4gb is probably gonna be enough for most games.
The 980, 980 ti and 390x are great options if they are in you're price range