The only mouse I have is the logitech g502 se and i was wondering if runs could still be valid if there is no scroll wheel active like using 3rd party software for remapping it? I dont use scroll wheel anyway for it anyway.

Also are non legit copies of the game allowed like stolen ones (No I did not steal one) My friend has one and they were wondering if that was allowed aswell as they want to get into the speedrunning

If you completely disable the scroll wheel there should be no problem, just show the rebind for it in the video submission. I would generally advise against using pirated copies for a multitude of reasons from copyright infringement to there not being any guarantee the version isn't tampered with, you can refer to the resources page for a link containing all valid Cookie Clicker links for different versions of the game.