It requires "a heat source of between 1,900 to 2,400 degrees Celsius, or up to about 4,300 degrees Fahrenheit" -- so your Nvidia gpu should work great for this purpose :)
No, but you could realistically make a small Stirling engine that would act as a heatsink for your processor while generating electricity.
Would be noisy as hell, but quite a cool project haha
Sure, you get ~40% back once you hit 1,900 to 2,400C
Only if your CPU is producing around 1,900 to 2,400 degrees Celsius