>Can I get some confirmation on this baker's?
>Every 12,500 years or so the Sun refreshes its outer shell, which is currently burning and giving us warmth and light.
This is not consistent with a current understanding of solar physics. The temperatures and pressures required to achieve nuclear fusion occur in the core region of the sun or any star, not the outer 'shell' or photosphere. Stars do form 'shells' or layers where fusion occurs, but this is usually after exhausting their hydrogen. Shells of fusion of heavier elements, like helium, occur near the cores in stars experiencing an advanced stage of stellar evolution, depending on the initial and residual mass of the star.
There may be issues with solar output of a cyclical nature, but your explanation is inadequate.
>Every half cycle, 6000Years+-, the earth's core flips over inside the earth
Are you sure you mean 'core' and not a pole reversal of the earth's magnetic field? These are common in the geological record.
>Can someone confirm my thoughts?
Unfortunately, no. While much has been withheld from us there are basic physical processes that are well understood.