I´m reading every post and i saw that there´s a post in wich says that it is. But in the "submit run" section it only allows me to select Gamecube.

Yes Wii is allowed. I'm sure almost everyone plays on the Wii due to the load speeds and potential crash of the 1.0 version in the furnace section. My guess is they just opted to keep it as GameCube on the site due to it being the format of the game, opposed to like a Wii shop version, etc.

This is correct, Wii is perfectly fine to use, everyone uses Wii for runs. Also yes, its GC on site because the game came out for the GC.