For this to work you need a display to send through the network, but that display needs not be a physical one. So depending on your definition it can be run headless. If you meant without it being plugged to a display then yes, if you meant without having graphical stack installed then no (there would be no point to streaming display without a display).
It works brilliantly on my Linux host with a 7800 XT, I think you might have an unrelated issue.
No, I cheated. I figured out that it needs to be solved in layers, and figured out how to solve the first two layers,but could never figure out how to solve the top one. Eventually I looked up how to solve it and reproduced the movements. I can put it in order now, but I wouldn’t say I solved it since I’m doing movements someone taught me not that I figured myself out.
Last year I would have said Arch. I have been running it for over 15 years with some small breaks to try stuff, or with some machines that have company issued OS. But I have been toying with NixOS, and honestly I’m loving it. If I had to choose only one and couldn’t change it it would have to be Arch, I know I can get 5 years with it easily, but if I was setting a new system today it would almost assuredly be NixOS, I might regret that 3 years down the line when there’s something I can’t get to work, but the more I play around, the less likely I think that would be, and the more comfortable I feel that I will eventually migrate to NixOS fulltime