As far as the source cues, they were written by Joseph Williams. Lapti Nek was written by him, Yub Nub, The source cues from Episode II, the two variants of the Dex's Diner music... and I think that's it... although I'm not sure who did the source for the Opera house in Episode III. My guess is Joseph Williams, John Williams son.
Who, btw, is the singing voice for the adult Simba in The Lion King strangely enough... even though Mathew Brodrick is quite the accomplished singer lol...