Second: Yes. 4k displays exist, but are incredibly expensive. The main REAL benefit for having the capability of 4k display is it means you can do HD 3D video as well (given an HD 3D display).
Yes, I don't doubt that they exist

My question was is it within the realm of possibility that the hardware in the PS4 would be able to deliver 30-60fps for demanding games at 4k resolution? A desktop GPU that can run games at that resolution is rather expensive.