Me, and probably the majority of all other physicists who might join that thread (again).
How is the question "what happens to earth without sun" related to elliptical orbits? What about parabolas and hyperbolas, the other solutions of the Kepler problem?
The sun is not the exact center of our solar system - it is quite close in terms of the center of mass, however.
The trajectory of the sun is determined by the gravitational influence of other objects (and partially by its mass ejections, but that is not relevant here).
The sun always attracts earth (and everything else), and we are not on a collision course.
This is just plain wrong. Eccentricity is independent of the mean distance to the star. See Kepler problem
Fixed point where? Which circular path do you mean, and revolution of what?
In order to get a superposition, you have to isolate the system from its environment. The box stands for that isolation, while a real box would not provide sufficient isolation anyway.