Your first two questions don't make sense (to me).

Originally Posted By: Bill S.
If for example I were to produce an azimuthal equidistant projection centred on the UK, with a radius of about 500 miles; then do the same from the opposite side of the world, such that the two boundaries were co-incident, it could certainly not be inferred that the rest of the world could be fitted into the same space as the UK.

That is correct and no one ever said that this was inferred.

Maps that preserve distance (equidistant) are never area-preserving.

Earth formed from a collision
www.preearth.net

Plate-tectonics is wrong
www.preearth.net/plate.html