Is it legal to submit speedruns done off of this cartride or do i need to purchase the games separately? Or if someone can point me towards where the rules are as i can't find it ... ty

This is a case by case basis for the game. Check the rules for the game or ask the game mods.

This is all as far as I know, and I might be wrong, but;

I don't think Speedrun.com makes a police checking if games are or not original, although the community doesn't encourage Piracy for sure.

I think the cartridge issue is the same as a console. If the game runs differently in a non-original cart or console compared to how it would do in the original then there would be a category problem (like being considered emulation for example).

So in any case check how the forum of the specified game thinks about it.