1. We should not scribble in books in the library.

2. We should not write down in books in the library.

3. We should not make a noise in the library.

4. We should not walk making sounds in the library.

5. We should not tear books in the library.

6. We should not stand on the table in the library.

7. We should return books in due date.

8. We should read books sliently in the library.

9. We should return books to the right places.

10. We should not chew gum in the library.

11. We should not wear a cap in the library.

(Are the expressions all grammatical? Correct errors, please.)

1 - fine

2 - delete "down"
3 - delete "a"
4, 5, 6 - OK
7 - "by the due date" (not "in")
8 - OK, but watch the spelling of "silently"
9, 10, 11 - OK

The expressions you provided are mostly grammatically correct. However, a few minor corrections can be made to improve the sentence structure:

1. We should not scribble in books in the library.
2. We should not write in books in the library.
3. We should not make noise in the library.
4. We should not walk loudly in the library.
5. We should not tear books in the library.
6. We should not stand on the table in the library.
7. We should return books by the due date.
8. We should read books silently in the library.
9. We should return books to their proper places.
10. We should not chew gum in the library.
11. We should not wear a cap in the library.

These corrections make the sentences clearer and more concise while maintaining their original meaning.