1) What RAM pages can I use within programs without having any bad consequences?

Even numbered pages are execution protected by default, so executing code here will crash your calc. That said, you can definitely store data. On the calcs with USBs, page 83h has some data that should be preserved or restored in the first 128 bytes. Just remember that any OS routines that interact with memory or variables expect the right pages to be there.

Ram Pages (WikiTI)

2) When an appvar is less than 16kb and is archived, will it all be on the same ROM page?

No, you can't expect this. Variables won't cross sector boundaries (groups of four RAM pages), but they may cross pages.

3) Can you interface with headphones beyond simply sending them signals with the ring and the tip? If so, how?

I don't know what you mean by this, sorry :| If you want to use headphones, you have to interact directly with port 0.

Yes, bcall(_fillAppBaseTable) should be sufficient.

What do you mean by the edit buffer? Edit buffers can be fairly complicated to work with.

The home screen does have a 128 byte buffer reserved as a copy for each char on it (16*8) called textShadow. There is another, similar buffer called cmdShadow that is intended for programs to use to back up that data.

For those two 128-byte buffers, you can do whatever you want with them. Worst case is that the home screen displays garbage. You can just fill it with spaces manually or preferably through one of the bcalls (I believe bcall 0x4546 is the bcall, but I forgot the name and I'm on mobile so it's a pain to search).

Oh, you probably don't want to work with an edit buffer for a task like that!

The data is stored in the program named !. (That's an exclamation point). Just locate the variable, get its size and locate the end if the program.

Just remember that if you replace a 1-byte token with a 2-byte token, you'll need to increase the size of the var (use InsertMem and manually update the var's size bytes) and vice versa.

I know that I'm 2 weeks late to the party (and several months if you count it from the original post) but I actually did something pretty similar to what you are trying to do a while ago. If you want to mess around with the homescreen input, you should use a homescreen hook. (http://wikiti.brandonw.net/index.php?title=83Plus:Hooks:9B8C) Since you mentioned hooks already, I assume that you already know how to use them. If you use the mode when A=2, then you don't have to worry about edit buffers and you can just open prgm! and edit it like anything else without worrying about edit buffers and such. If you want to change what a key sends on a double press by using the mode where A=1, you are in for something much trickier. It is simple to change B to the keypress that produces the token that you want. If I recall correctly, you should change keyExtend to the second byte if it is a two byte keypress.
The problem is with removing the previous token. There is an edit buffer command to shift the cursor one token to the left (BufLeft) so that might work, and then you could call BufReplace to replace that token that was previously typed in with the one you want to change it to and then return nz to ignore the keypress since you handled it manually. I don't know how this would work when the user is in insert mode.

Oh, you might actually be able to do that relatively easily. If there is a getKey code for the tau token (you'd have to look it up, there might not be), then you could use a getKey hook to override a [PI] keypress.

Then you also have a parser hook that replaces all of the tau tokens with 2pi before passing it back to the OS parser. The nice thing is that 2pi takes 2 bytes and tau is a 2-byte token, so you don't even need to resize. I don't think the parser hook has a mode for when a program ends, so you won't be able to re-replace the 2pis as taus that way, but you could probably make your getKey hook do it!

EDIT: there is in fact a ktau in the ti83plus.inc ! You'll want to use the RawKeyHook and the Parser hook.

Oh, you are right about that. That would be a little more difficult as you would have to resize variables.
When the parser hook triggers mode 0, the name of the program being parsed is in basic_prog. You could first scan for all tau tokens that can be directly replaced (and replace them), while counting all of the ones that need extra work. Then verify there is enough memory to insert an additional two bytes for each remaining entry. Use InsertMem at the end of the program, but remember to adjust the variable's size bytes as well as basic_end. Finally, replace the remaining tau tokens with "(2pi)".

It is a complicated process, so good luck!