Learn English – Is it impossible to say “I am busy on every Monday”

True. But then, if we want to talk about the banana tree's part individually (though all), we use each and not every.

BBC clarifies it-

We tend to use each if we are thinking about members of a group individually, and every if we are thinking of them in total.

Compare the following:

We gave each child who came to the party a present. We handed them out one by one.
We gave every child who came to the party a present We gave them all a present.

Found the exact phrase from the book Hawaiian Heritage Plants where it says each part is usable one or the other way.

I am too busy to realise [that] John is depressed.

As you suggest, this sentence is grammatically correct but, logically incorrect: if you are too busy to realise, you don't know that John is depressed.

What you are far more likely to say, on finding out that John had (for example) attempted suicide, would be:

I was too busy to realise [that] John is depressed.

You are probably still busy but the news is much more important than what you are doing, so you are no longer too busy to realise.

It is OK to omit the that in informal spoken English, but it is better to include it in written English.