Got to ask: There's option on PS2 menu to fasten the disc speed. Is it okay to use this on PS speedruns? I had to ask because emulators are 'ok' (yes, filterable), when pc's run usually faster than consoles. Or will it it go on emulator part?

I think it's fine. Regardless of disc speed, Playstation runs will never be faster than PC and there's always IGT to approximately judge which runs are faster without loads.