AppVars are application variables that store data for either programs or applications. AppVars usually store data that may include high scores, preferences, etc. However, there are some programs that require the specified AppVar(s) in order to run it. These kinds of AppVars usually store a variety of information such as maps, sprites, etc.
It is fine if you delete an AppVar of a deleted application. However, if you choose to reinstall the application, some high scores or preferences may be reset.
Considering that the TI-84+SE has about 24KB of ROM/Archive, I wouldn't worry about space memory. Remember, you can run all you programs from archive if you have a calculator shell such as DoorsCS7 or MirageOS.
With that said, you can use AppVars if you are creating a Hybrid Basic program or an assembly program. DoorsCS7 has the Celtic library where you can create, access, or modify AppVars.
There are no such things as "finance appvars". The Finance application is built into the OS.