Well, first off, which is better:
Assuming you’re fine to make the product, then get sued by Unity a year into it and lose all your time and money.
or
Asking Unity first.
As for how to do it - do you understand game development? If you’re asking basic questions about C#, then you aren’t ready to tackle something as complex as a game engine. Judging by your questions, you’re a LONG ways from being able to start your project.
An account would require a database connection, which means a basic back end in PHP or .net and understanding of SQL. Saving is ambiguous. You can write to a serialized file, use system.io to save in xml, or use a local sqlite database. There are other options as well, or you can write your own.
Nobody can really tell you which way is the best way because we don’t know what your ultimate goal is. However, if you’re dead set on doing this, I recommend:
Don’t try to ship a modified version of Unity as your own product. Instead, make game “templates” for the asset store. For example, an RPG template with all the controllers, save functionality, conversation system, etc already built into it. This way, someone could buy the uRPG template for $50 or whatever and essentially be able to drop their models into the scene, apply a handful of scripts, and go.
Then advertise your templates the same way you would your game engine, similar to how Tornado Twins push FPS Controller.
That being said, if you are new to programming, then this is shooting yourself in the foot. You really need to at least make a couple of games and actually learn efficient coding and how to use Unity before trying to sell that ability to other people.