Windows: Is it *possible* to create a (virtual) video card driver?
I'd say it's definitely possible, since that's what virtualization tools do for their guest utilities, but I wouldn't be able to tell you how in details. I'd suggest looking at the VirtualBox guest driver code as a starting point: http://www.virtualbox.org/browser/trunk/src/VBox/Additions/WINNT/Graphics
(This is released under GPL as far as I'm aware.)
It's definitely possible, see for example the UltraVNC mirror driver. But I don't know of any virtual video driver that makes source code available.
I have been searching for something similar and I found a nice solution: spacedesk. You can download it here: http://spacedesk.ph/In windows, it installs an extra monitor, which you can open in a browser or a viewer. Enjoy!