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Works on the flat earth model as well
No, it doesn't. If the Earth is flat the sun has to rise and set at the same time for all location on the Earth simultaneously. This is an easy test to do at home with a flashlight and a flat piece of cardboard.
No, it travels in a circle. You haven't even looked into it at all because your questions are already answered. Stop thinking of the sun in the heliocentric model where it is huge and far away. In the flat model it is inside the firmament and the same size as the moon and the black sun. It creates the seasons by tightening or widening its circular path. It only illuminates the area it is in, not rays that travel forever like in the ball model.
There is no possible way in three dimensional space for the sun to appear visible to one area of a plane while simultaneously not visible in another.
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