The moon is 2,160 miles in diameter. One light minute in km can be found by messing with the formula used in problem 2. You have to rearrange to solve for distance. You can't see the North Celestial Pole from the south pole. You can't see the South Celestial Pole from the North pole.
Winter days are colder because of the Earth's axis tilt.
The tilt also means the days are shorter so we get less sunlight. So the answer is 14 days. Plato, like most Greek intellectuals, believed the circle was the perfect geometical figure, the ideal form and a representation of Unity, and uniform motion about a circle was perfect motion. Since the heavens were perfect all celestial bodies must move on uniformly on circles. Copernicus needed epicycles and deferents because he was using circular orbits not elliptical ones.