Hence the refinery, the addition of carbon in certain metals can either make said metal stronger or weaker depending on what percentage.
No a carbon planet is where rather than a nice balanced ratio of oxygen to carbon it is carbon heavy, resulting in a the existence of giant latices such as graphite and diamond. Earth is (if i'm remembering correctly) a nice balance of Nitrogen, and oxygen (atmosphere) with a core of silica, alumina, lime, magnesia, iron, sodium, potassium, and water (crust). With carbon only really being found as a compound with something else rather than just pure carbon.
Also not a coreless planet per say, one with a very weak core, like lithium, would practically have no EM shielding.
From what I understand almost everything is made up of some carbon..... so every planet is a carbon planet(?).