*other* than during a game (ie. hitting Enter), how can I send a message to my opponent?
One of my games with Mag is broken, I need to tell him to repair it (repairing on my sided didn't work).

Go to the Personal Challenge menu as though you were going to challenge that person. When you click on his or her name, instead of clicking Send Challenge, click Send Message instead. A popup will appear, in which you type your message, then tell it to send it.