Short answers, pulled from the story.
Planetary differentiation is the process by which a planetary body's chemical elements separate into distinct layers based on their density and chemical behavior. Dense materials such as iron sink toward the interior while lighter silicates rise to form the crust. The result on Earth is a layered structure with a metallic core, a silicate mantle, and a thin outer crust.
Planetary differentiation is driven by heat from radioactive isotope decay, the energy released by impacts during planetary accretion, and gravitational pressure inside large bodies. Once rock melts, denser materials can sink and lighter ones can rise. The short-lived radioactive isotope 26Al is thought to have been the main early heat source.
Planetary differentiation has occurred on planets, dwarf planets, the asteroid 4 Vesta, and natural satellites such as the Moon. The compositions of certain meteorites called achondrites show that differentiation also took place in asteroid parent bodies.
Differentiation produced the Earth's dense iron-rich metallic core, a less dense magnesium-silicate-rich mantle, and a thin outer crust composed mainly of silicates of aluminium, sodium, calcium, and potassium. The crust has a density of roughly 2700 kg/m3, the mantle roughly 3400 kg/m3, and the planet as a whole averages 5515 kg/m3.
KREEP is a distinctive basaltic material found on the Moon that is high in potassium, rare earth elements, phosphorus, uranium, and thorium. It is thought to be a chemical differentiate trapped between the lunar crust and mantle as the Moon's primeval magma ocean crystallized, occasionally erupting to the surface.
The Moon's density is substantially less than Earth's because it lacks a large iron core. The Moon most likely formed from silicate-rich material splashed into orbit by a large impact on the early Earth, at a time when differentiation had already concentrated Earth's iron toward its interior, leaving the ejected material iron-poor.