I would also like to add that the practice of reffering a queen in her own right as "king" was also common up to the middle ages. Examples include the first swedish queen, reffered to as "Kung" instead of "Drottning"

Most persons forget that the UK was not just the set of islands it is now. The war would hinge on North Africa and the middle east. If the germans got a secure hold on egypt and palestine, the British would eventually be forced to surrender to stop the bloodshed.

My opinion is that it is correct to call it the byzantine empire, since the empire was ruled from the city of byzantium. We must still remember they were the descendants of the romans, so the roman empire is applicable, but it is less specific