Before you can choose whether to use a singular or plural noun with any, you need to know which of the various functions and meanings it has in the context in which you are using it. In each of your affirmative sentences any is equivalent to every.
It can be found in any / every book.
This can be understood by anyone / everyone.
It can be said in any / every language.
For this reason, the following does not work:
? It can be found in any / every books.
In the interrogative sentences any does not mean every. In fact it does not really have a meaning at all and could be omitted:
Do you have books?
Is there a rule?
As to whether the singular or plural should be used with uncount nouns, the plural is more common:
Do you have any children? - ? Do you have any child?
Do you have any books? - ? Do you have any book?
But if you are expecting there to be only one of the thing in question, the singular may be used. In other words:
Is there any rule?
may be said in expectation that there will be only one rule.