It is still possible to download individual songs, but it's not easy. One way is to start downloading the album and while it downloads the first track, choose the track you actually want to download. Hit stop on the other track. Or, create a playlist with the track or tracks you want to download.
To see which tracks are downloaded to your device, go to the Music Settings and turn off Show All Music.
jaysue - I agree that deleting songs looks to be complicated. I don't see that unobtanium's method works - even when I turn off Show All Music, I still can't delete tracks. The only way I see is to go to settings --> general --> usage where you can delete all music at once. Anyone else know anything different?
Edit: Reading some more threads and it appears that some people can delete individual songs when Show All Music is turned off and others can't. I'm in the latter camp for the moment; maybe it takes some time to update when you turn that setting off.