So Lucifer, the Light-bearer, the greatest angel thinks he can outdo God, probably could've, gathers billions of other angels, starts rebelling, God sends them all to Hell? Or Earth?

After that, how is Lucifer(Satan) the price of Darkness? If he is the Light Bearer? What makes him a False angel other then the fact he thought he could out do God?

Lucifer/Satan was basically just an invention of the church to scare people in the Dark Ages into being faithful; it, just like everything else in the bible, has contradictions and errors. Though, an explanation could be this: the original sin (Eve taking the fruit) was the act of gaining forbidden knowledge; the light-bearer represents this knowledge. God says this knowledge is evil, so the church tells the people that it is evil, and Satan carries this knowledge, so he is evil.
Or something like that; I have to read up on it.

Satan was jealous of God and wanted to be God but in doing that it is a Sin. He took a third of the angels with him cause they him instead of God even though God and his two-thirds left of angels were a whole lot stonger besides God wins by default! Hence angels like us have free will to serve God or not! And besides the tree that Adam and eve ate from was the tree of the "Knowledge of GOOD and EVIL" -just like finding out how to rob a bank! I hope this helps.