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... is called a Great Circle arc.
It is simply called the distance between the two points - simple as that. How that distance is measured will depend on the nature of the surface on which the two points are located as well as on the metric for measuring distance that is defined on that space.The common metric in Euclidean space is the Pythagorean distance while on the surface of a sphere (like the Earth, for example), distances are measured along the great arc.
Because the earth is round and the bottom of the earth is smaller than the middle of earth such as the equator
A compass
No, the centre of the Earth is called the Earth's core.