Can i run this game on the port in my metroid zero mission cart?

I'm not sure if it's allowed or not but if it's not allowed, I would say it should be because GBA is listed here on speedrun.com as a platform the game was available on.

If it's seriously different you could make a different category but I say it should be allowed for sure.

GBA version is allowed, as we already have at least one time on the leaderboard that was done on that version. To my knowledge there's no advantages or disadvantages of playing GBA, except that Up+A is not possible.