To answer the general questions.
Some kind of native emulator/hypervisor with a view to savestates. Afraid not. I can get you stuff for cheats (see GBAATM, gabsharky and various other things, though mainly stick with GBAATM), for slowdown (not sure if GBAATM has the feature right now but it would be easy enough to do the basic CPU flood method as seen in DS flash carts and DSATM), for soft reset (GBATA should have this, if not BOMA), for sleep patches (GBATA again, though for the EZ4 you probably want to instead have a look at what Kuwanger and I think Dwedit might have done for it) and a few other choice things that exist as the logical consequence of those things just mentioned but savestates are not an options.
In theory I might be able to pull something off but I would so much rather have some hardware on the flash cart side of things to help me out there -- the EZ3 (the EZ4's basically direct predecessor -- in the menu it is called EZDisk for a reason it is that close) had savestates, nowhere near emulator grade mind you, but they never made it to the EZ4 and no other worthwhile flash cart (you might be able to find a supercard, unfortunately you would then have to deal with a supercard trying to do GBA and that was never good) you might be able to find today has such a feature either. Likewise no GBA flash cart ever had terribly reliable savestates -- if you were around for the early days of on hardware DS savestates then it was probably better than the GBA ever got.
Password saves... there are certainly some but I have not encountered it as a real problem for most games I might play. What would ultimately be far easier than some kind of generic, or even game specific, savestate engine is to hack the games in question to use a save. It is considerably easier to do on a GBA than it was on older systems, not trivial but if it is not for a silly kids game (I just did a quick search and that is where most seem to be, aside from the obvious things like the GBA video series), so something like Back to Stone* I could see it being worked up for. The general idea will be the passcode is just a means of encoding binary data, it will then have something to decode it and if you can instead feed it something from a bit of SRAM you just made appear (it is always there, well documented and not controlled by a bank switching setup or anything like you might see on the NES, SNES, GB/GBC or anything like that) then you have your save, likewise you will want to be able to catapult the passcode into the SRAM as well but that should not be so hard either. Whether you want to go all in and remove the passcode features is a different matter... personally I would leave it and call it a "backup for those that want it".
*by the way anybody have that passcode generator for Back to Stone, release thread for the generator
http://gbatemp.net/threads/password-generator-back-to-stone-u.40851/ ? We (myself and various others) could not find it when looking for it a while back when the game was the game of the week selection (
http://gbatemp.net/threads/gbatemp-game-of-the-week-85.340895/ ).
GBA emulators for the DS that are not on an enhanced flash cart like the iSMM or DSTwo, you are pretty much limited to the ichfly GBA stuff already linked (
http://ichfly.github.io/gbaemu4DS/ ) which is a fantastic proof of concept and some great coding but not really ready for prime time, there is some older stuff but it is even less developed/capable. I am not sure how much further the DSi specifics ever got for that sort of thing.