When the PlayStation 4 came out, I liked the DualShock 4 so much that it shook me to my core. Was it possible the redesigned analog sticks and the fancy touchpad were going to help the PS4 controller ...
While you can't permanently delete messages on your PS4, you can use the "Leave" command in the Options menu to remove messages from your screen.
To add friends on a PS4, go to the Friends menu and search for the person you want to add. You can also accept friend requests on the Friends page.