Proof? What makes you think that you know the density of the sun?
Quite simple, you just need to know the size and mass, easily found in many sources on the internet and in books. However, if you have to ask me to spell it out for you I shall in a new topic. The average deinsity of the sun is however about 1.4g/cm
3. You still haven't explained how such a small FE sun can initiate and sustain fusion, and before you ask if I know the density of RE sun, how about showing how you know the density of FE sun.
Even a small change in an angle has a large effect over tens of thousands of miles. A change of three degrees may seem insignificant over a sheet of A1 paper. But that same change of angle projected over a square mile becomes extremely significant.
But you claim the sun is now spherical, therefore it emits light in spherical wavefronts. Refraction is a result of light slowing down/speeding up as it passes from one medium to another, but the shape of the wave front remains spherical. That means that if the sun were hovering at the other side of the flat earth, light would hit the atmosphere further and further from the sun at an ever decreasing angle, so the overall refraction would be less and less, so the light would reach the ground anyway. Light from the sun would hit the top of the atmosphere above my head at a shallow angle, only after it enters the atmosphere would refraction begin. Refraction can only bend the light to the normal, since after it becomes vertical it doesn't refract, so the light hitting above my head, even if it did magically super-refract, it would still land on me.

So night could not possibly happen in FE. The suns light, since it travels in all directions, will hit the atmosphere at the right angle in the right place to get to the ground on the side of the earth that should be "dark".
Snell's Law also applies to the light of the moon and stars. This is why the moon is not visible at all times over a twenty-four hour period. If stars were visible during the day they would also not be visible over a twenty-four hour period. When the celestial bodies are on the opposite side of the disk, tens of thousands of miles away, all of their light has been refracted into the surface of the earth. Therefore they are invisible to the observer.
Yes, but I extend my argument as above. I have seen the moon during the day, near the horizon (where the sun would appear at night in FE theory, so the same magic superefraction should apply). But at night, the same magic superefraction should apply to the light of stars near the horizon. But guess what, it doesn't!! During a solar eclipse you can still see stars, even though they are "on the other side of the flat earth." That's how they measured the bending of light around the sun, by looking at stars near the sun during an eclipse.
The sun's effect on the RE is like a spotlight, however it illuminates half of the earth exactly. FE sun could not do this, since a) the reasons stated above and even if you invent some more fantasy science to explain this, and b) a circular light cannot exactly illuminate half of the FE. You can't illuminate exactly half a circle with a circle, and I don't mean half the area, I mean half the circle itself.