this had probably been asked a few times before, but to have a fast run is linux needed? thanks

No, 1.001 PC is actually faster if you can get used to inputs on that version, but most runners prefer inputs on v1.001 linux instead

1.001 PC is not faster than 1.001 Linux. 1.00 can be faster than 1.001 Linux due to some glitches that were patched in 1.001, but 1.001 PC is slower than both 1.00 and 1.001 Linux with no benefit.

You can also run 1.001 Linux on Windows, and that's what most runners end up doing. But I would definitely not suggest using 1.001 PC in any case.