The reason is that these definitions are all in Japanese. Here are a few: https://kotobank.jp/word/近日-481223. You’ll see this further down the page:
It’s definition ①. In 大辞林 (which is sadly no longer online), you have this:
Definition ② refers to the recent past. I guess it’s probably a little less common that the meaning that refers to the near future though.
Oh, most certainly, but what I meant is that it’s hard to make statements related to what will happen a few years down the road with certainty. That or, well, perhaps the future has a tendency to feel further away? That might be why 近日 is fine, but 近年 might intuitively feel a little strange if used to refer to the future. 近い means ‘close’, after all.
You can do that if you like. It sounds helpful. My personal approach would be to remember that 先日 exists as well, and that in languages, competition has a tendency to push one word out of the way. But that’s because I want to remember that both meanings exist, especially since they both exist in Chinese (which I also speak).
Perhaps. I’ve never tried searching for papers on this sort of usage. I’ve found some on more widespread structures like 〜ば and the way it’s used in different contexts.
Technically speaking, you use hiragana for きた here, because it only has a grammatical function here, and doesn’t preserve its original meaning (‘to come’, as a physical movement from one place to another). (You could probably keep the kanji form for something like 行って来る though, since the literal meaning is preserved.) It’s the same reason you technically should write こと and not 事 unless you’re using an expression like 事を起こす (‘to cause trouble’), because こと is usually just a nominaliser and nothing else. In practice though, these technical rules aren’t very important outside of perhaps formal contexts. (I have no idea if I’m right though, because I’ve never studied Japanese business correspondence.) What I can tell you is that the plastic entrance chips they give you at the Hamarikyuu Gardens in Tokyo clearly use 「下さい」after a て-form (I took a photo of it), whereas you should technically only use the kanji version with after a noun, so frankly, people probably don’t care too much.