They're orbiting around the earth at those speeds, but the relative speed difference between two objects orbiting the same planet could be anywhere from 0km/s all the way up to the combined orbital speeds of each object(i.e if both objects are going 15km/s, then the max possible speed they could whizz past each other is 30km/s), depending on which direction the objects are traveling.
Think about cars all traveling the speed limit(say, 40km an hour) on a straight road. The cars going the same direction as each other have no speed difference, they're moving relative to the earths surface, but relative to each other they're not moving at all. The speed difference with a car going the opposite direction, on the other hand, would be 80km an hour.
Deep space ships also wouldn't look like futuristic planes, because aerodynamics are only needed to escape earth's atmosphere. Likely we'd be building deep space ships in space, so as not to waste fuel breaking the atmosphere. Borg cube is more likely.
Corners would suck in space unles the structure wasn't pressurized. most ships would probably be a series of tubes. They would also need to spin to allow any sort of gravity, unless we invent anti-gravity tech.
There may be parts that are pressurized tubes but cubes have more storage space than cylinders of the same size so the overall structure could be a cube.