How would recent oil price decreases have affected an Independent Scotlands economy?

Not at all, the first minister Alex Salmond was always unable to explain how much money Scotland would get from the North Sea oil revenues.
In simple terms the D.T.I. sells licences to drill, and then the taxman takes a cut of the oil landed from the wells as tax, this amount would have been the same before and after as fuel prices at the pumps do not reflect income for the state.
Fuel duty tariffs at the pumps would be the same, Scotland would have (maybe) collected this tax, the amount of revenue collected would be reliant on how much fuel (and therefore tax) was bought in Scotland.