Say, is it okay if you have to something like Retro Arch for emulators?

Of course, if I was to set rules, I would have to be clear on what is allowed.

I had to bring that up because I know someone is going to try to use any cheats. I rather just go for trial and error, before trying any speed run.

My advice: if you're going, set a speed run challenge that allows a cheat, please point out what is allowed and mark it.

Rules about emulators are game-specific (so are a lot of other rules too). You should also know that Retroarch is just a operating system for starting emulators. So there are a lot of different emulators installed by default on Retroarch.

Example: let's say the game you want to run only allows emulator A. Then you have to check if this emulator A is available on Retroarch. If it is not you can try to install it manually. You should not run the game on emulator B for leaderboard submissions. other case: In some games no specific emulator is mentioned in the rules. Then you can choose whatever emulator you like.