2

If you add a new Gmail address to your Gmail contact list, is that person notified that they were added to your Gmail contacts list? Both people have Gmail.

5

No. That type of functionality is usually (read: virtually always) exclusive to sites with social networking functionality (like Google+, Facebook, LinkedIn, Tumblr, etc.), and any functionality of that type is seldom found in anything beyond sites specifically designed for that purpose (exception: IM/chat).