Can I use British pounds in Frankfurt airport duty free shops? Not particularly concerned about exchange rate
No guarantees, but I have noticed that most duty-free shops around the world will take just about any currency
as you said it may not be the best exchange rate but you could probably get rid of your pounds there
use plastic which is accepted everywhere, otherwise they will need to do a funky conversion
Credit card unless you want to use up your FX currency.
I would put the amount spent at duty-free shops on the credit card and save the GBP for the next trip to London.