Since it is a Z97 it should support VT-d.
for your processor, you are probably speaking about the 4790S, and it should support it
http://en.wikipedia.org/wiki/Haswell_%28microarchitecture%29
Gigabyte VT-d support is not the greatest, Asrock is doing much better.
You can build a machine that will do both, your video card will stay at standard idle power consumption unless you start the VM that uses the video card.
Here is a link to the setup I built : http://www.michons.us/2015/01/14/esxi-whitebox/
To the extent of my knowledge radeon R9 290 do not work with ESXi. (see vmware forums)
a good article to read for GPU passthrough : http://www.pugetsystems.com/labs/articles/Multi-headed-VMWare-Gaming-Setup-564/
Personally I am passing through an XFX radeon 7850.
There are none, with the update, you are only upgrading the vibs that have a lower revision number than the ones in the image you are installing.
That's what people with whiteboxes use.