You’re right in that the origins of Japanese are still not clearly understood. However, I do recall a native Korean speaker once telling me that when he learned Japanese, the grammar was exactly the same, just that all the worlds and reading were different. Importing words is one thing, but grammar’s not something you can import very easily, and Japan’s colonial rule wasn’t enough of an influence (look at Taiwan ), so I believe they are largely the same. But that doesn’t rule out other influences such as the Polynesian ones.

P.S. From what I’ve heard, those researchers doubt the connection of Japanese/Korean with the Altaic language family, which was an older theory linking the two. I understood it to mean that Korean/Japanese/Ryukyuan were a language family unto themselves. :-/

I often say that the Japanese were very unfortunate living off the coast of China/Korea, and not the coast of Europe, as the English did, because then they would have picked up the Latin alphabet the way the English did, and saved a lot of English-speaking students of Japanese a lot of trouble in later centuries!

And I want to underline your point that learning kanji takes a lot of time and practice. A good way to learn the Buddhist virtue of patience and fortitude. Reading a lot of varied materials and (if you’re in Japan) seeing them on many signs as you walk around the streets is important.

As for the phonetic component, I’ve noticed this too, though I wasn’t sure if it was just a coincidence. In my kanji studies for JLPT3, I noticed a few similar looking kanji all had the same “on yomi”, which now tells me it is not just a coincidence.

My favourite example showing onyomi and kunyomi for the same kanji is illustrated by two words that mean the same thing, but the kanji inverse and the reading changes
切腹　seppuku
腹切　harakiri
both mean slitting one’s belly in ritual suicide. Seppuku is on-on and harakiri is kun-kun.

Two further points about readings.
Onyomi can be further broken down into when the word arrived in Japan (in 3 waves I think). I believe Japanese dictionaries also give this information. I doubt it is widely known or studied in school however. And I would have to look up a book (I don’t have here) to give you any examples.

To return to radicals. A significant proportion of kanji use radicals as a phonetic component rather than a semantic component. Therefore it is possible to make educated guesses about an unknown kanji’s potential reading. You can also group kanji by shared phonetic components and readings to help you remember them.
形声文字 (85% of kanji)　have a semantic component and a phonetic component
for example 寺　in these kanji gives the on yomi ji (but no semantic reference to a temple, perhaps other than one that is made up )　時　侍　持
(but note not in 特 doku or 待 tai)
Again unfortunately I’ve never really come across a reference that spells this out for all kanji in a systematic manner.