The choice between singular and plural in sentences such as "They have different book(s)/age(s)..."

I am confused about the use of number(s) in some sentences. I have come up with several types and made some sentences:

1. In the sentence above, should I use “the use of number” or “the use of numbers”?

2. In the case of some concrete objects which are identical, if there are two people, each of them has a book. The books are physically separate but their content, size, etc. are identical. Should I say “I share my book with my mate, while they use different book.” or “… use different books.”?

3. And what if the books of them are also different in content, as well as physically separate?

4. If I am asking about two words. Each word has only one meaning. Should I ask “Do they have different meaning?” or “… meanings”

5. The case of individual attributes, such as age and sex. I have seen a sentence on Marriam-Webster “Some people are reluctant to reveal their ages.” Here we have age in plural, and on Linggle there are also a plenty of examples of “their ages”, while there are even more cases of “their age” in singular such as “Two 3 % ) did not report their age.” and also for sex “The undergraduate students and TAs also reported their age and sex.” Is there any difference between the use of singular and plural in such cases?

6. If there are two people of each has only one goal, and I don’t know if their goal(s) is/are the same. Should I ask them “Do you have different goal?” or “… different goals?”