Dear NT:

You wrote:

1-Everybody didn’t have a book.

Can’t this sentence mean two things:

1a-Not everybody had a book.
1b-Nobody had a book.

Yes, that is why no English speaker would ever say that.
An English speaker would say either a or b.

2-Each of them didn’t have a book.

This is very awkward English. No one would speak this way.

Can’t this sentence mean two things:

2a-Not each of them had a book.
2b-None of them had a book.

Truly, NT, no native English speaker over the age of six would likely every say either sentence 1 or 2.