Question

Identify the italicized part of the sentence. As well as being a competent secretary, Lauren has become the informal club vice president.

Answer 1

I think that the italicized part is "the informal club vice president" or just the head of this prase: "president".

This is a predicate nominative. A predicate nominative is a phrase that follows a linking verb (here "become" and describes the subject or renames it.