Chris' Q: Although we are not the true end-user, we are instructed by our end users what to play, so we know exactly what was played. How would Shoutcast know what Stu played (if that's who he uses), unless they are streaming it themselves? And yes, we keep track of everything. The standard rate for an internet broadcaster is approximately 0.11 cents per listener per song. If one person listened to it, you could get about 900 songs for a dollar, or if 900 people listened to one song, it would cost you a dollar.
Argo's Q: It would depend on who the music is published with, what deals the publisher has negotiated with that producer, etc. I'm contractually bound not to reveal the rates my company pays, but it less than a cent per listener per song. However, on something like Jeopardy, where the number of viewers is in the millions, you can see why Merv wanted to be the theme writer.
On a side note, did you know the theme to Star Trek has lyrics. Even though you've never heard them, by Gene Roddenberry adding them after the music was written, he became a co-writer of the song, and eligible for royalties.
Excellent article here on how it all works:
http://entertainment.howstuffworks.com/music-royalties.htm--Mike