furigana - Homographs: how to deal with them?

For example:

• 一日{いちにち} = one day (duration);


• 一日{ついたち} = first day of the month.

First of all, are the meanings correct? Because I found contradicting answers.

I suspect the meanings are overlapping in some cases?

Then, after a quick search, I found out that okurigana is efficient to disambiguate them. Didn't the author mean furigana instead? Maybe I didn't grasp something here.

Lastly, what are the most important (to know)/most frequent homographic Kanji out there?