Is the Queen of England genetically related to William the Conqueror?
Yes, Liz II’s name is included on one of the pages at this site which attempts to list as many as possible of the descendents of William the Conqueror. By the way, I never knew, until I read it here, that ‘William was the illegitimate son of Robert I, duke of Normandy and Arletta, a tanner’s daughter. He is sometimes called “William the Bastard”‘.
I would have thought that most people in the UK (and thus, Australia, USA and Canada, etc) are genetically related to William the Conqueror. Going back that many generations, the question doesn’t really make all that much sense. Going back 50 generations, I have 1.12×10^15 ancestors. Even allowing for duplicates etc, the chances are that everyone in the UK in 1066 who had children is one of them.