I could be wrong, but I don't think that's how it works. You're comparing the true size of UK with the flatmap projection of US. To do what you want, you need to compare the true maps of both countries - with the cities.
No, because this map scales the country according to its latitude. So when you drag down England to be next to Atlanta, you're looking at the size of England with respect to Atlanta. The "true size" is just "true" in comparison to whatever it's on top of. So it should be accurate.
Ok yes. An accuracy issue then as it's probably using a simple algo for the projection. Stand corrected.