I have an experiment for the first. Start 2 people at the equator 1000 km apart. When they reach the north pole, measure the distance between them.
Then there is geodesics. Consider an aeroplane. The most efficient method of travel from point A to point B is a straight line. However, when this straight line of travel is transposed upon a sphere, it is not straight at all. It is geodesic. This is the explanation for the proposed experiment. If the Earth is flat, the two individuals will never meet. If the Earth is a sphere, they with converge at the apex.
Let's meet at the equator and go for a walk. You owe me a beer if we meet at the top. Cheers.