Welcome to the wonderful world of scooter ownership!
1. This could be material from an improperly seated gasket. Depending upon which one, it could be the cause of your oil issue. 2. Could be the belt, variator or clutch. I'd pull off the cover and observe the movement of all three. Compare to some YouTube videos and see if one or the other is evident. If not, I'd start with replacing the belt first, then the clutch assembly. 3. I've had great luck with
http://www.scrappydogscooters.com/ but there are other places that advertise here on this sight that I've read good things about.