[mujina]

First: I feel so happy that you guys are taking an interest in the subject! Hoping this can help more people down the line.
Also: It's exactly as EastEriq said about the similar-looking characters, that part is likely as it should be.

What may be discussible are all the exotic latin replacements. I can't imagine a Japanese reader running in romaji words with Ɯ, ǻ, Ƿ and the like....

Quite right, I suppose they were trying to cover all the bases (or used a different language file as the starting point). At least (if I understand correctly), those extras will just never get used, but they won't impede the functionality.

If you can't see any Japanese characters I would start with changing all the separators to the ones used between the lower and upper case roman character keyboard layouts, recompile and see whether it has an impact.

Thank you, tried it just now. Just to check if I got it right: I replaced both the second ~ - and the - - with ~ - followed by two blank lines. No change, though. So far, I've been making up for the lack of keyboard by just scrolling down through the suggested words.
But, since a native-character keyboard would definitely help the dictionary, I'm continuing the discussion here, though the keyboard part may be slightly off-topic.

I wonder (total ignorant here, so it may be a silly idea) if the keyboard doesn't work because the number of Japanese characters is higher than the number of keys on the standard QWERTY keyboard? Or (and i think this more likely) it's not be supposed to work that way, by simply mapping a character to a key.

This is what other virtual Japanese keyboards do: The characters you see in keyboard.txt are syllables - well, not quite, but it's the closest thing. か is ka, ね is ne and so on. To write か, you don't press a specific key; first you type a "k" and the keyboard writes in a k provisionally (or just waits). Then, if you type an "a", it writes a か (and suggests other characters that have the "ka" reading, like 家, 火, 歌...), or a く and the alternatives if you write a "u" after it, etc. etc.

I've tried the Chinese keyboard that comes pre-installed, and it works the same way Japanese ones do (I don't know Chinese, but the workings should be very similar). I've attached a picture, so you can see it takes input from the regular QWERTY: I've written "chuu", which has temporarily been input into the search box, and on top of the keys I'm given a selection of characters which have the "chuu" reading and which I can tap to input and search them.
Just how it does that, though, is a mystery to me. Prompted by another thread here (thank you, @EastEriq!), I've looked into system/language/keyboard and system/config/global.cfg. The first only contains files for EN, IT, RU and UA (so not even for all the languages that come with the device). The second does include a line that reads language=ZH (which I'm taking to be Chinese), but the following lines are nothing I can make sense of. (I can copy-paste the content of global.cfg if anyone is interested.) The device doesn't even have a Chinese dictionary, but it must keep all those characters somewhere.

Also, I remember someone saying on some forum that they only got their Japanese keyboard to work after switching to the pre-intalled Chinese keyboard, then switching back to the English one. Odd.

I've attached a .zip with 1) the accessory files (with the extended, "better" collates.txt, but the other two are directly from your JaK folder, Markismus), 2) the .xdxf JA-EN dictionary, which, iirc, I converted from the awesome JMdict, and 3) the resulting .dic dictionary for Pocketbook.