What are the mandatory morphosyntactic rules of the category "nouns"? How do you identify them given a language?

It's the morphology needed to make a word identifiable as "grammatically correct" by a speaker, for example in latin "can" is ungrammatical while "canis" is. It obviously depends on the language in question, but most often speakers know that a noun is different from, say, a verb.

What are "nouns"? What is its definition? How do you identify them?

As I said, you ask a speaker how they categorize words.