I can't add any friends to my friends lists nor can they add me. Despite this i get updates on what they're doing on my Mass Effect 3, so something is happening.
Have both of you exited Origin and logged back in since trying? Also to be on the safe side, please make either of you don't already have 100 friends.
Could you please go to the this page, make sure that you are signed in and ensure that your email is verified and that you have your Security Question set up.