Doesn't exist, at least not in a very fragmented underground way. From experience, this sort of thing gets sorted out in private messages assuming your contact wasn't immediately scared by the much more draconian copyright laws (sometimes this is overstated - most people into retrogaming used roms and emulators off the internet, even new in-house nintendo developers) and aren't a collector interested in hoarding it.

Cave Story DSi is a bit special because it has the involvement of a Japanese indie who released it for free and Nicalis, but none of the established publishers (Nippon Ichi) involved in the 3ds remake, so the legal warnings aren't as big. Good luck about games like the collection of Nintendo Game Seminar 2007 projects (DS Download Play) and the 2014 ones for Wii U. Common underground ways to find similar content like Ｓ●●●●　probably won't work because the Japanese warez scene shares the same general disinterest in DSi preservation.

You might probably find people who can speak English, but it doesn't always necessarily mean they are comfortable writing in it. You'll still need some Japanese fluency (not just for the search, but also the conversational aspect where courtesy, even attempted, goes a long way) and no, machine translations are as useless as when it's used commonly the other way around.

It will be very hard. Just look at the situation with Japanese J2ME games made for the MoJa (DoCoMo i-mode) standard - there are dumps floating online in both jar and jam formats and some simulators for them, and youtube videos of them in high resolution, but i have yet to get my hands on one legitimate game (just screensavers so far) even though i know they exist and are shared somewhere online.