On the first about the Space Station - and besides Carol's offering of checking out certain websites that list the details of its locations at specific times, which is very helpful in orienting one's self and looking in the right direction at the right time - using a telescope to follow it across the sky certainly defines it being what it is.
There are not two of them up there that are the same size and shape, just as there are not two Saturns up there that are the same size and shape. When I see either of these things, I know I am seeing them for what they are, the one circling Earth; and the other circling the Sun.
The second thing about mapping is certainly interesting, and I have had quite the little journey with understanding how the ancients could have understood our spherical world, and turned that understanding into a flat map that made sense. Certainly they could have made sections that were spherical, depicting the landscapes so that several images would depict Earth's surface that could be imagined as a complete representation of Earth; but turning those depictions into a flat, rectangular map is quite the extension and achievement in understanding spherical geometry and spherical trigonometry.
Besides Gerardus Mercator developing a technique that has come down to us from the 1500s, the ancient Greeks developed a way to depict sections of our curved surface into 2D, flat images of our surface. The technique was similar to Mercator, and relied upon both spherical geometry and trigonometry.
But like many things the Greeks understood and developed, they first learnt the hows from elsewhere, and mostly from ancient Egypt. That kind of trick certainly beckons the question: Did the Egyptians develop it, or learn about it from elsewhere too?
(Certainly possibly just theory though, but still thought-provoking)