How does the friend list work? What are the limits?

You're able to see all your friends in the social bar at the lower edge of the screen. The tab on the very right contains all your friends and here you also have the ability to add more friends and accept friend invites from others.

You can send invites as long as your number of friends is under 80. and you're able to have up to 140 friends at once. Keep in mind that you won't be able to send new invites until you're below 80 friends again.