First of all: I’m not sure about all things concerning DSi. Parts of the text below may be inaccurate or even wrong. I wrote it to the best of my knowledge.
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As far as I know the Japanese version does not offer additional languages for “Launcher”. The DSi has a region lock – but this is only active for DSiWare and the very few DSi exclusive carts. DS games and DSi enhanced games are region free.
Non-Japanese games most likely don’t contain Japanese language and most games will fall back to the English default instead. Manual language selection is only possible in few games because of…
No idea?!
Maybe the flashcart firmware/kernel supports enforcing different languages for the games. I don’t know. My AceKard 2i (AKAIO) does not do it; at least I could not find anything.
What definitely is possible: Installing custom firmware and replacing the normal Launcher with TWiLight Menu++ . This
does support setting languages for each game and for the menu itself. You could use it instead of your flashcart
or to launch your flashcart (if supported) with different language settings
or both.
When it comes to modifying the actual firmware on the DSi NAND… I would rather not do this (unless you have a hardmod) and I have no idea how to do it. The next best thing to modify the normal Launcher menu is
FreeNAND. You would have to obtain files from a US or EU DSi in order to use it.
Don’t ask for such here as those files obviously contain Nintendo copyrighted material. Keep in mind that the normal Launcher does on HiyaCFW (SDNAND/“EmuNAND”) only works when less than 2GB are free on your SD card.