since you can smith stone with no plans does that include Random Rare Stones or is that just for the basic stone? also what all kinds of rare stone and rare metal is there

Rare stones and metals are formal components. They are also VERY small - so there is no real possibility to craft an item out of them; there is also no reason to. To actually find out what rare components are out there, you will have to ask in play, but unless you cast formal or intend to, they don't do anything.

If you look through the Rules section and/or Item Lists, you can find a list of all the known smithing material types.

Iron, steel, jade, argent, aureum, banesteel, wolfram, and maybe some others, are all smithable metals (or stone in Jade's case).