1) Money no object and power no concern. DSTwo, DSTwo+ or their 4 in 1 thing. You might still be able to find one but they got harder to find a while back.
Alternatives
Whatever R4 officially supports Wood and does not have a timebomb. Don't know what that is right now.
Possibly the acekard 2i , though they are not the best hardware quality.
EZ5i maybe. They stopped updating shortly after the big DSi/3ds flash cart killer update (it would be a while before the 3ds was fully hacked and could disable the protections that way) which meant a handful of later releases would not work on stock firmwares. There was some talk of open sourcing things like they did with some other stuff of theirs but no movement yet. You can probably also use the anti piracy patches people use for compatibility layers to make things work (it mainly being stuff like pokemon conquest and black 2/white 2 that people seem to care about, most other things released after that also working fine as the EZ5i had some pretty nice countermeasures).
In terms of features this is probably one of the few things to compete with the DSTwo family (though obviously no onboard emulation boost) -- it has pretty decent (for what they are) savestates and in game text reader. That said most of the others will do
cheats, soft reset and load which is all most want.
GB/GBC is emulated well enough on anything.
SNES natively is more tricky. You can get some stuff done and the DSTwo and other enhanced carts with their onboard stuff do better, though far short of something like the PSP. Generally if the game had an acceptable PCE/TG16, megadrive/genesis or GBA port (including with ROM hacks to enhance them and sort issues, of which there are many issues and fixes) then do that instead.
2) 4 main choices you will be reasonably able to find.
EZ4. Was the main choice until everdrive and EZFlash came back with modern designs. Lacks some of the niceties of those titles but will play just about everything as it would have happened on hardware.
http://gbatemp.net/threads/buying-a-gba-flash-cart-in-2013.341203/page-18#post-4756995 being the main tricky titles (note this is not a list for the supercard stuff I mentioned elsewhere, though some might still be troubled).
There are many iterations now, just don't get an EZ4 lite compact.
EZ 3 in 1.
EZFlash Omega.
Everdrive GBA stuff.
Definitely don't get a supercard GBA slot cart or a clone thereof. I have not seen a firecard clone in some years now but they might still be out there but when they say 128Mbit (or 256 in the really rare cases) they mean that size -- if you are not used to Mbit then divide by 8, so 128Mbit if 16 megabytes and GBA games go up to 32 (list of said 32 meg games in the link above, though some hackers use the extra space as well).
Older EZ4 models might do for RAM for homebrew but if you really want rumble and memory then it is probably going to be the 3 in 1 you seek. Good lucking finding a GBA size version (repro makers, people wanting a real cart for their ROM hack and apparently some electronics types that noted it used a chip they really liked and was hard to find otherwise rinsing the market of them years ago, to say nothing of everybody mostly wanting DSlite stuff back then).
For pokemon transfers I would sooner rip a save and use an emulator, or recreate it with one of the save editors.
3) and 4) The DS Slot is too slow to run them natively so anything has to be emulated, which the DS lacks memory and speed for. The GBA slot runs things in GBA mode natively so if you have a vaguely usable cart (which is to say just about everything that was not a supercard or clone thereof) then if it fits then it runs.
For the DS slot stuff then consider it a proof of concept rather than something you will want to use if it is just the native DS emulators.
If it is on the supercard dstwo family, ismm or iplayer then the onboard emulation they provide (all said carts have fancy CPUs on to do their own thing) mean you can do most of the library pretty happily. Some of the really annoying to emulate stuff like Golden Sun might trouble things but they are few enough in number you can probably get away with it.
5)The EZVi is not the EZ6 but the DSi compatible version of the EZ5, and last iteration of the EZ5 family to continue being supported (the originals, NYE and plus versions dropping off at various points).
https://hackmii.com/2010/02/lawsuit-coming-in-3-2-1/ if you want info on what the DSi workaround was.
The EZ4 was originally a cart aimed at running DS ROMs (it took a while for DS slot protocol and encryption to be cracked) but inherited much of the GBA compatibility of the EZ3 (of which it was essentially a version of, but without RTC, with DS mode and with a mini/micro SD slot depending upon the version rather than NAND. Also lacked some of the nicer features of the EZ3 like compression and savestates).
6) Yes you can cut edges and attach a pull tab, make a new 3d printed case for it or cannibalise an old game (I am duty bound to use barbie horse adventures as an example in such discussions as a joke but all GBA games are more or less the same unless they have extra hardware).
64 vs 32 is not going to do much for you as nothing outside of the EZ5 line (and even then some hard to come by betas kernels for it) supports the extra NOR space. Not to mention most things only need the RAM.
Many flash carts added native support for the 3 in 1 (EZFlash released the code for it) but if not then there is DS homebrew to support it. Most people would probably use Rudolph's exploader program.
7) For your purposes then not really -- it mainly being a package to add support for the 3ds. There might be a store out there somewhere with some but you are somewhat late to this party so good luck on that one.
8) Not on a DS, no (there is substantially more hardware for the DSi than there is on the stock DS). I don't know what ended up going for flash carts and the DSi in the end (for the most part it was only Team Cyclops that did anything other than make a DS flash cart that booted on a DSi and even then support and functionality was iffy). Today most people doing things with the DSi either do it on a 3ds or with a hacked DSi firmware (which itself can be a bit trickier to get sorted, though I have not kept up with the very latest developments there).
9) Devkitpro (specifically the devkitarm part of it)
https://devkitpro.org/ is what most would use for low level programming. Quite a few people had some fun and made good stuff with lua but they were far more limited than what you could do with that.
Supercard DSTwo does have some more capabilities if you want to develop for that, though be warned it is rather hard coding (most people ignoring the DS side of things and just taking inputs and feeding back video and outputs).
Other than that pretty much anything you can boot into DS mode with will have a DLDI patch/support built into it. DLDI (or perhaps more technically libfat) is was what used to access the SD card in the end and make sense of the dozens of flash carts and new ones coming on the market.
Some people making
cheats quite liked some of the action replay PC debugging and then supercard dstwo/ismm real time memory viewers/editors. However today we have very nice emulators so minimal need for that one.
10) Don't know what French flash cart sellers have survived the various purges, bans, paypal/credit card wranglings and whatever else, and they were never particularly numerous to begin with (not to mention most technically being in the French speaking parts of Belgium if memory serves). Sweden then has
https://www.shop01media.com/index.php?route=common/home , though their stock is pretty slim pickings these days. They are a good site though and have long been seen to go out of their way to make things work.
11) Nothing easy I can point at and say this. There was never the equivalent of a GB player, super game boy or even transfer pak for the DS or anything compatible with it.
It would be easy enough to solder on things to the DS like people use to make turbo controllers, PC controller adapters and whatever else if you really wanted. For the pokemon typing game we also saw a hack to use a network pipe to mimic its keyboard option. I don't know what, if anything, DSserial provided and it would again take game level hacks, and I would sooner use the GBA slot of that sort of thing (see what guitar hero did, though more advanced for this).
Short version you are going to need to open up the DS, find the debug points for the controller (or something akin to it) and solder wires to them. From there you can do any of the old game controller to USB adapter type, turbo controller, split controller, disabled person controller, hacks to get buttons presses from one of those to register on the DS. The easier way would be to wire directly to it, the harder would be have some kind of interface (an arduino or teensy type programmable chip being more than capable of this sort of thing) and plug in a normal controller and adapt accordingly.
12) Most people these days looking at playing DS games on the 3ds family are not using a flash cart as much as the DS compatibility layers for them (see the long threads we have on anti piracy patch databases for use with them) and running them from SD cards. Even then you can run older versions of the DS layer that don't have as much flash cart detection to use the older stuff, or possibly even drop it entirely but I have not looked into that. Most modern R4 clones, Acekard 2i, or any of the DStwo family will do here.
I held back a bit there for some things but hopefully enough is there to answer what you needed. You might also like this thread
https://gbatemp.net/threads/current-favored-kit-for-ds-dslite.537988/ as many of the same questions were asked and some we went into a bit more depth for.
