You can't listen to your Rhapsody library even though it exists as a file on your computer and the most recently listened-to songs are also on your hard drive. If you'll notice, they don't need to download after having downloaded once. I'm sure this expires at some point.
The reason you can't listen except while running Rhapsody and being connected to the internet is that Rhapsody checks your rights to listen to these songs almost constantly.
You can purchase tracks for $0.49 per track (in addition to you monthly fee) but they will only burn to a CDR, not download. There is probably a way to emulate a CD burner so you could "burn" to your hard drive but I've never tried.
You CAN, however, use your Rhapsody subscription from any computer that has the Rhapsody application installed and is connected to the internet - even if it's dial-up. The first time you use it, it will take a long time to get started (I think it's a function of the size of your library) but once it does start, the next times are faster.
You can also E-Mail playlists to yourself that will activate Rhapsody as soon as you click on the link that comes with the playlist.
Hope this helps. I've been using Rhapsody for over a year and have no plans to cancel.
CVIII