Hi there,
1. You would need to create a custom field for each author. A plugin like Advanced Custom Fields (ACF) should help you do that.
Then you can:
1. Create a Hook Element: https://docs.generatepress.com/article/hooks-element-overview/
2. Set the hook to after_archive_title
3. Add the necessary code from ACF into the hook, and it should display the email if set in the user profile
4. Set the Display Rules to the author archives.
2. Beside where, exactly?
3. Not too sure what you mean by “as profile”. Can you explain a bit more?