fellow Japanese lovers! I've been studying Japanese on my own for a few months, and have reached the point where I have a question that I can't find decisively asked or answered anywhere. I'm hoping that someone with more experience can provide an answer on this site. My question is not simply when (or if) to use ON or KUN. Rather, I want to know if it is grammatically acceptable to switch arbitrarily back and forth between using ON and KUN--as well as between using Hiragana and Katakana--in speaking and/or writing Japanese sentences? Again, there are two separate considerations about which I am asking. Is a transverse usage pattern among all four elements permissible for purely arbitrary reasons, or would it represent poor grammar? And, if the latter is true, how does one decide when to use which pattern or combination thereof? Thank you to anyone who can clarify for me.
Firstly none of this is about grammar. I have edited the question tags. Now on to the main question.
The choice between katakana, hiragana and kanji is only relevant in the written language. It is possible to write everything in hiragana or katakana, but it would make it rather difficult to read. For example, some books for young children are written without any kanji because they haven't learnt them yet. Personally I find that this slows down my reading because it isn't so easy to see where words begin and end (there are no spaces in Japanese sentences).
You could randomly mix up the kana and kanji in some abnormal way, maybe for artistic purposes, and it would still be readable, but I think rather awkward depending on how extreme you have been.
The choice between on-yomi and kun-yomi is about speech rather than writing. Here you must decide how to pronounce a given kanji. There is very little flexibility here. If you make the wrong choices it will render your speech almost/totally unintelligible.
There are no guaranteed rules for knowing whether to use on-yomi or kun-yomi readings. This link explains a few general principles though.
It depends on words. You read "1,2,3" and "1st, 2nd, 3rd" as "one, two, three" and "first, second, third" respectively, not "fir, sec, thi" and "onest, twond, threerd". Japanese is similar in this regard.
Some words share the same kanji with different reading. e.g. 剣｛ケン：sword in general, つるぎ：double edged straight sword ｝However, most words don't have reading variation.