Is there any rule to use nouns in the sentence, the rule like subject verb agreement? Is It any rule for verb-noun agreement, one noun to another noun agreement, and noun-preposition agreement?
No, there is no such rule in the general case.
The subject-verb agreement refers to the number implied by the subject, and the number implied by the verb. For example:
The boy eats an apple.
The boys eat an apple.
Both of these are grammatically correct, but "The boy eat an apple" and "The boys eats an apple" are both grammatically incorrect in all cases.
Perhaps by verb-noun agreement you mean that
The boys eat an apple may be taken to imply that the boys are all sharing one apple. In this sense, verb-noun agreement might mean the sentence you actually want is:
The boys eat apples.
This is not a matter of grammar though, but semantics - what you are trying to say. There is no rule that can help you here.
Noun-to-noun agreement would not make sense, as each noun is independent of each other (there may be one boy and many apples, or many boys and one apple, or many boys and many apples).
Noun-preposition agreement also does not make sense, since prepositions do not imply any number.
The book is on the desk.
The books are on the desk.
In both these examples, "on" stays the same no matter how many books or desks there are.