Is it ok if I use a fake copy of Pokémon Red? Everything seems the same, including the glitches. I know it's fake because it says Game instead of Gameboy.

Most of the fakes are literally just flash carts with the ROM version on them (aka what you download and use on emu). So yeah they should work for speedruns. Interesting question though, ive never owned one so I cant say if it plays totally the same.