I did this for a while with a 3080 and a a770. It works well, but after a while (and new Nvidia drivers) I switched fully to Linux.

• yes the GPU needs to be unused by Linux to allow for passthrough. There are some guides for making single GPU passthrough work but I never went down that road.
• see first response, making the Nvidia card available to both Linux and the VM is a hassle I never did. I would just game on Linux with the a770
• two separate PCs for the most part. I used udev rules to have Ctrl L + Ctrl R switch my input between devices
• pipe wire and udev rules. However audio is painful I actually used a USB physical switch to pass through things from host or VM. I would just pass through a USB controller to the VM and those USB ports on the back would be exclusively for the vm