Can a male author write stories with a female protagonist well?

First off: This is not intended to be a sexist question. I have no desire for debates on sexism on this question.

Secondly: I am not referring to romances/love stories, but rather to a more realistic story about everyday life, such as depicting the life of a female college student.

Thirdly: By protagonist, I mean a main character; the hero(ine). Love interests, supporting characters, and villains do not count as protagonists

Thanks for understanding.

My question has three parts:
1. Whether a male author can write stories with a female protagonist with deep characterization and with accurate depictions of thoughts and feelings when (1) there are gender roles in society; (2) such gender roles influence the way people of different sexes think and behave; and (3) a male author will likely see the world from a male perspective.

2. Whether there are any techniques that a male author can use to fairly depict a female protagonist.

3. Regardless of your answer to 1 and 2, whether you believe that a male author should be writing stories with a female protagonist.