does the speedrun need to be for the whole game or can it be level by level? I'm using Kega Fusion and have no way to time it. is there an outside way?

It will vary from game to game, The game(s) in question would have an option to view full-game runs or individual levels on the lefthand side of the game page. Livesplit is the best way to time runs imo, but you can [usually] use anything so long as it's accurate.

It depends on the game :

Some games have Individual Levels categories (wich are a separate part of game leaderboards also), for these, you can do speedrun of just one level. Otherwise, there's the usual full-game part of game leaderboards, wich usually have Any%, 100% and such. For these, you have to check the rules, but it's usually finishing the entire game.

As for timing, if the game you're speedrunning doesn't use in-game time, you can use programs such as LiveSplit.

Also, i feel like you're referring to a specific game, if that's the case, maybe asking the moderators of said game would be better (or just asking on the game's leaderboard forum directly).

If you dont want to use your computer every time you run, you can use FramePerfect Speedrun Timer for mobile in both Google Play and App Store. It is easy to learn and easy to use.