I'm not altogether sure that is a 'genuine' WWII PFF badge, Robin. Certainly, this
is a real one...
Note the difference to the top edge of the wings. However, post-war copies usually do not have such fine detailing of the feathers, which yours has.
I've put 'genuine' in inverted commas because the subject of PFF badges is quite thorny. It was an 'unofficial' award and certainly most were manufactured by Gaunt's in London. However, there is no mark on the actual badge and I believe that other manufacturers also produced them. So unless you're fortunate enough to find one on its original card backing it's virtually impossible to be certain....
As to the rest of your most interesting badge, I haven't a clue and would like to know the answer myself !