>>what kind of documents are necessary to be able to teach Italian in the USA or UK?

Question

and for private school ?

Answer 1

In the U.S.A.

To teach at a college or university level you would need a PH.D. in Italian from an accredited university.

To teach at a middle or high school you more likely would need to have a State's teaching certificate.  Italian isn't a popular language to learn in middle or high school.