The moped doesn't have any model name anywhere I can see. If your moped has a delorto carb like mine does, it has a big round thing that the air filter is hose clamped onto, and says 'delorto' on it somewhere. This is very simple, there is only one screw and it adjusts the idle speed.
the 'starter clutch' i'm talking about is the clutch that engages by a lever in order to pedal start the moped. It would either be part of the centrifugal clutch or a different part and it looks like it would be covered with oil like the rest of the stuff in the transmission case, so it makes sense that thicker oil would help. I haven't taken it apart yet and when i do i'll have a much better idea exactly what part is worn down, what it looks like and what it might be called.