Implementing a Versus Mode would be an enormous overhaul, if possible at all. In either case it would require a hell of a lot of experience with SNES programming.
As a beginner, you want to start with something small, meaning you either hack a very simple game, or you make some minor changes to a game that you like. As you are poking around and making these small changes, you will stumble into deeper areas and learn a bit more than you need to know at the time.
Continue this process, taking on a bit more work for each iteration, and you'll find yourself making slow but steady progress. This approach is broad and applies to many things, but a major point here is that giving up gets you nowhere, while continued effort gets you somewhere.
For starters, make some visual changes, since this is as simple as it gets. Improve some fonts, refine some shoddy graphics, that kind of thing. After that, try finding text in the ROM so that you can change it. If you find yourself losing motivation at this point, then it's time to stop and question how passionate you are about your project, because this is just the tip of the iceberg.
I'll take a look at the ROM later and let you know if anything is compressed, because if it is, then this is not a starter project.