Could you please let me know if there is a way to activate email notifications when you receive a contact request (and when one user confirmed your request)?
Within CB > Configuration > Connections adjust "Notification Method" as needed.
Also, is there a way to add a pop up to on the user profile, or a little sign (like the numbers on a Facebook page) that indicates you have a connection request (or someone confirmed you as a friend)?
You can have a new connections indicator in your login module. See your login modules parameters to enable it. The workflows module also has the same functionality. Currently we don't have on-site notifications so no a Facebook like notification is not available yet.