Good answer. As you saw, (b) and (d) make no sense here. The difference between (a) and (c) is that "over" doesn't lend itself to quantification in the way that "above" does. Without the quantifier "320 kilometres", either one would work.
By the way, thank you very much for citing your source. Unfortunately, The Best doesn't live up to its name. Once again, their example sentence is extremely poorly written. Even though it is not technically incorrect, it sounds hideous.
The worst problem is the redundant use of "the earth". This is easily corrected:
2: 320 kilometers above the surface, a space station will orbit the Earth.
I find this sentence perfectly acceptable, but I would like it even better if it were inverted:
3: The space station will orbit the Earth 320 kilometers above the surface.
I hope you found this helpful.