GIVE ANSWERS - English

Firstly, note that we use ”There” to tell someone that we are describing the position or existence of something.

”There is a book on the table.” - ”is” is used here to describe the position/existence of a single item, ”a book”.

”There are books on the table” - ”are” tells us that there is plural or more than one item we are describing the position of or existence, in this case ”books”.

BUT!

”There is a book and pens on the table.” - we use ”is” because the first item in the list is singular, ”a book”.

and

”There are books and a pen on the table.” - we use ”are” because the first item in the list is plural, ”books”.

The next part of your question:

”Books are on the table.” and ”There are books on the table” communicate different things.

”Books are on the table.” communicates the emphasis that ”Books” are our primary focus. The location of ”books” is secondary to the object ”books”.

”There are books on the table.” - our primary concern is on the position (and perhaps even introducing the existence) of ”books” .

This is a good question. The usage of there is and there are depends on singular and plural. However, it has some nuance as well.

There:
... is a book
... are many books

If you are unsure, you can use the example you provided.