Standard Personal Belief Disclaimers apply.
No, none of this is Biblical (I'm a Deist - we don't do "bibles" other than the word of God as writ in Nature) and my only source is what I remember.
Lucifer and Satan are indeed different. (Though I'll skip the back story and focus for once.)
"Satan" is Samael's title. I don't believe that he's evil or that he rebelled against God. I believe that he is the angel who was cast out by Michael in the first War. (With Lucifer's leap - NOT Fall - being the second, and the rousting of the Grigori being the third.) Those loyal to him were cast out as well.
Samael did what he did because God asked him to - he was partially created to become this entity (among other things), and when the time came, God asked him if he loved Him enough to fulfill his purpose. Samael, being so loyal and so loving, did as he was asked, even though he knew he would be reviled for it and would cause a rift in Heaven through his choice to serve. (And yes, I believe that angels have free will, if they choose to exercise it. It Samael had told Alaha "no," a different angel would have said "yes," even if this role wasn't part of his original intent.)
I believe that Alaha asked Samael to play this role because humans have free will, and untested faith is faith without strength or foundation. Like all things worth having, I feel that we must work for our convictions, and Samael plays the role of the devil in order to help us do so.
As for the entity described in churches, the evil master of Hell who roasts and torments souls forever, I believe that he's a human construct layered over Samael's being in order to instill fear and therefore gain control of the congregation. We see what we expect to see; we make the devil as terrible as we need him to be to satisfy some inner hunger for horror or to inspire ourselves to believe through fear. I think it's the same instinct that prompts us to look when we drive past car accidents. This doesn't mean that this version of the devil isn't real - I think that it's more than capable of tormenting a soul beyond the point of madness, if that soul allows itself to be tormented.
As a side note, I don't believe that the devil or demons possess human being. I think possessions are performed by enraged ghosts, for lack of a better word.
In my LJ, I wrote a fictionalized version of Alaha asking Samael to assume this role. Here it is if you're interested: http://amariune.livejournal.com/2878.html
"Someday after we have mastered the winds, the waves, and gravity, we will harness for God the energies of love; and then for a second time in the history of the world, human beings will have discovered fire." - Teilhard de Chardin