Why did god create satan?
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He is an evil angel, and, IMHO, an exceedingly unpleasant being (who apparently takes great pleasure in his work) but who is ultimately subservient to G-d.*
His mission is to try to deter people from doing G-d's will. G-d wants us to resist Satan and thereby become better suited to be companions of G-d.
The Zohar compares the Satan to a harlot who is hired by a king to try to seduce his son, because the king wants to test his son's morality and worthiness.
The story of Job details this well.
- The angels, even ones like Satan, while given almost free reign, lack ultimate free will, in that G-d can tell them what to do, if He is so inclined. This is probably the great distinction between Man and Angels, in that we can do whatever we want, if so inclined (although it is unwise to so do.)
Kind of deep question.
I'll try and explain simply.
There is eight things humans will do in heaven forever (without being bored) - know and love God, angels, each other, and ourselves - forever we do this, we do this by 'peeling layer after layer' like an onion learning more and more deeply about each of the four. Now, angels do the same thing, but in the hierarchy, which is Heaven, they are below man.
Angels have more powerful minds and wills than man (this is compared to the weak mind and will of man on earth, not our regenerated bodies in heaven), but their rank is absolutely vertical and always below man's rank in Heaven. They were created to serve man and this upset some of the angels (about 1/3 of them), as even though they were created with a more powerful mind and will and they were created before us they were our servants.
Now, Lucifer was the numbero uno angel. Meaning his mind and his will was most powerful, second only to God himself (though a distant second). God created the angel Lucifer to know and love God more deeply and thoroughly than any other creature created. He was one of the angels in the first choir (maybe even made up a choir of just himself) that was filled with fire (this has nothing to do with hell, or the phenomena of fire that we know, this is filled with the passion for God so fierce that it beats the worst kind earthly addictions). His purpose was to know the mind of God.
Simple answer: God created Lucifer to know His mind and to be the highest servant of man.
so God messed up basically...
and if lucifer who became satan was the originator of sin, then how did he become sinful? What influnced him...
I guess you can say that.
He became sinful because he became proud, he put himself above God (not actually). He knew what torment it was to disobey God intuitively, yet still did it. This is because sin is not reasonable, it was illogical for Lucifer to basically create evil and it is still illogical to sin today. 
 Kreeft, P., Angels and Demons, (SF: Ignatius Press, 1995), p. 64.
I don't understand how something all-powerful, all-knowing, etc. would/could make a mistake?
I thought God made everything to be perfect?
Nope. We failed the test.
I am not talking about us. My question is about Lucifer. If there was no sin before him, then how can something come from nothing;) and cause someonme to be sinful?
no, and this topic is not in regards to creationism.
Well, it's about us.
Satan's job was to tempt us.
G-d created Satan to tempt us to sin.
Now, Satan may (or may not) like his job too much --- to the point that he could be logically be seen as "rebelling."
But Satan is serving the function for which he was created.
Again, Satan's job was/remains to tempt us and refine us (by freely rejecting him and embracing G-d, rejecting sin and embracing G-d's desires for us) so that we can be suitable companions with G-d over eternity.
Who said it was a mistake? Free will is one of the key doctrines of religion. You can't have free will if you don't have choices.
Like Yin and Yang.
Maybe it's your definition of perfect that is skewed.
While the following may not have been specifically written about satan, I think the principles contained therein apply to this discussion. I know this may not satisfy your want for why as they are statements of Authority and not explanations per se, but as for me, I have nothing to add to these words:
"Behold, I Myself have created the smith who blows the fire of coals and brings out a weapon for its work; and I have created the destroyer to ruin." Isa 54:16
"The LORD has made everything for its own purpose, Even the wicked for the day of evil." Pro 16:4
"All the inhabitants of the earth are accounted as nothing, But He does according to His will in the host of heaven and among the inhabitants of earth; and no one can ward off His hand Or say to Him, 'What have You done?'" Dan 4:35 (the words of Nebuchadnezzar after realizing God is God)
Your statement has nothing to do with what I ask...please reread
While I dont want to debate free will. For arguments sake I will assume there is free will. Still the question remains. Even though Lucifer had free will, there was no such thing as sin or anything related to it to tempt him.
So saying he had free will doesnt do much.
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How noble God is, giving us the freedom to do exactly what he tells us to do...
To inspire Dante, John Milton and whoever directed 'The Exorcist'.