It is the one point that does not move during rotation.
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They move in a swirly way
Moving a shape, without rotating or flipping it. "Sliding". The shape still looks exactly the same, just in a different place.
True.
In reality, the shape of rainbow is a circle. The center of the circle is an imaginary line between the center of the sun and the head of the viewer.
Even in a rotating restaurant, the kitchen would be located in the non-rotating center. If you had a kitchen on a rotating platform, the centrigugal forces would cause a certain amount of spillage and generally would make it harder to control the ingredients.