From what I know the sun (or any other star) nuclear fission keeps it from collapsing under its own gravity until the fuel runs out, if that's so why doesn't the earth surface like the tectonic plates collapse to the earth's core? is it because of similar processes that happen in the earth's outer core (nuclear fission)? and if so what would happen if they would once stop?
For the same (an more prosaic) reason milk skin floats over boiling milk - because it is lighter than the layer below. During the formation of the planet it went through a process called Iron Catastrophe, were a large parcel of the denser materials like iron and nickel sunk to the core, leaving the lighter materials close to the surface.
Nice graph with relative densities follow:
Fission contributes to keep our internal engine super-hot and well-oiled, allowing for our metallic core to spin and generate our magnetosphere. Eventually we'll run out of heat, the outer core will solidify and stop spinning.