Once a file reaches 100% it then needs to verify all the contents before LW moves it to the downld folder. So if you cancelled the downld before this process has finished then it will still be in the incomplete folder. Also if it detects a difference in the downld hash then it will try to downld that part again.

If your songs are missing their icon then you need to make a default for them. Use the same principle here for changing default except for audio & choose your prefered audio player: Setting Default video app

If you don't have a decent audio player then there are too many to suggest. A couple quick ones are: QCD: http://www.quinnware.com/ & also iTunes: http://www.apple.com/itunes/download/ or dBpowerAMP: http://www.dbpoweramp.com/