I actually do have two GPUs in my machine, but that wasn't my initial plan when I built this machine. I use the iGPU in my CPU to display my desktop and use my dGPU for Steam under Linux. When I want to run Windows I can unhook the dGPU from Linux, pass it through to Windows, and then both my Linux graphical session and Windows run at the same time. If you have a single GPU then the act of unbinding from Linux it to pass it through to a VM terminates your Linux graphical session (everything not under that graphical session keeps running) until you exit the VM and rebind the GPU to Linux.

As for the second part - yes. Typically you want to export the environment variable DRI_PRIME and set it to the index of the card you want to use to render and it will be displayed on the currently active display card.

The steps might be slightly different if you're using an nVidia card - both of my GPUs are AMD.