(I may have posted this into the wrong topic.)

To begin with, why is it that you can 't delete the finance app? I even tried a full reset. Could it be a menu (like the stat menu) in disguise?it's not as if there weren't enough open keys to place a finance page.
Next, How does an app add commands to the Catalog? If that can be cracked, then DCS and other shells will finally be able to post custom commands and give us back our commands.
Finally, where and how does it store its variables? they're not in any of the menus under [2nd][+][2]. in fact, the only way to access them is through the app itself. There's so much we can glean from this one app.

Technically, it's not an app, so that's why you can't delete it, and why you can't find those variables.

I'm sure someone else could elaborate a lot more than I can.

Good questions; the Finance app can certainly be a point of confusion:
1) Finance is not actually an App. On the TI-83 non-Plus, it had its own key (the [APPS] key was the [MATRX] key, and [2nd][MATRX] was Finance). Because the [MATRX] key became [APPS] starting on the TI-83 Plus, the Matrix menu moved to [2nd][x^-1], and Finance became an item in the Apps menu for lack of a better spot. Don't be fooled: it's part of the OS.
2) It stores its variables in specific RAM locations, rather than in the general UserMem area.
3) We actually do know how to add custom tokens, through a combination of the ParserHook and TokenHook, but it can be a twitchy business.