Is Satan brother of Jesus?

Mormons claim that the Bible teaches that all spiritual beings (including Jesus, angels, human beings and Satan) are brothers under God the Father (http://mormonvoices.org/1/jesus-brother-of-satan)  The key points of the argument are:

1. God is "the Father of all spirits" (Hebrews 12:9).
2. We are spirits, as are Jesus and Satan, therefore God is our spiritual Father.
3. If we all have the same spiritual father, then we are spiritual brothers of each other and of Jesus and Satan, and they too are spiritual brothers of each other.

Straightforward enough.  But the word "all" is not present in the Greek text.  A literal translation such as the ESV reads as follows:

Besides this, we have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live? (Hebrews 12:9, ESV)

All that this passage then affirms is that God is Father of some spirits, not necessarily of all of them.

A Mormon who was fluent in his Scripture might, however, point us to Ephesians 4:4-6, where it says:

There is one body and one Spirit—just as you were called to the one hope that belongs to your call—one Lord, one faith, one baptism, one God and Father of all, who is over all and through all and in all. (Ephesians 4:4-6, ESV)

Here it says God is "Father of all," but the question is "all what?"  All creation?  All living things (plants and animals alike)?"  All people?  All believers?  It doesn't say.  Given that this passage is part of a larger section that speaks to the church about the relationships that fellow believers are to have with each other, it seems most likely that, "Father of all" means "Father of all believers," in which case it does not support the claim that God is the Father of all spirits, or in particular, of Satan.

Jesus himself identifies "spirits" (according to the Mormon definition) whose father is not God in John 8:37-44:

"I speak of what I have seen with my Father, and you do what you have heard from your father.”  
They answered him, “Abraham is our father.” Jesus said to them, “If you were Abraham's children, you would be doing the works Abraham did, but now you seek to kill me, a man who has told you the truth that I heard from God. This is not what Abraham did. You are doing the works your father did.” They said to him, “We were not born of sexual immorality. We have one Father—even God.” Jesus said to them, “If God were your Father, you would love me, for I came from God and I am here. I came not of my own accord, but he sent me. Why do you not understand what I say? It is because you cannot bear to hear my word.  You are of your father the devil, and your will is to do your father's desires. He was a murderer from the beginning, and does not stand in the truth, because there is no truth in him. When he lies, he speaks out of his own character, for he is a liar and the father of lies." (John 8:37-44, ESV)

Here the Pharisees with whom Jesus is talking agree completely with the Mormons that God is their Father but Jesus denies it and identifies their father as the devil.  God the Father loves Jesus and tells the truth, Satan hates Jesus and tells lies.  Because the Pharisees do the things that Satan does, they show clearly that Satan is their father and not God.

If God cannot be Father of those spirits who hate Jesus and tell lies, can He be Father of Satan?  Obviously not.  What spirits, then, is Hebrews 12:9 speaking of?  Certainly the Holy Spirit is included in the group, for He is the spirit that pre-eminently loves Jesus and tells the truth.  In Revelation 1:4, 3:1, 4:5 and 5:6, the Holy Spirit is described as "the seven spirits", so it would make perfect sense if Hebrews 12:9 were understood to mean "God the Father of the seven spirits," or "God the Father of the Holy Spirit."  God is also Father of those who have learned by the power of the Spirit to call Him "Abba, Father" (Romans 8:15, Galatians 4:6).

But God is not Father of all those who call Him "Father".  The Pharisees whom Jesus addressed in John 6 called God Father, and he showed them to be mistaken.  Just as not all who call Jesus Lord will be acknowledged by Him in the end (Matthew 7:21-23), so also not all who call God their Father will be acknowledged by Him in the end.  "You will recognize them by their fruits" (Matthew 7:16).  These fruits will not be seen in their prophesying or casting out of demons or doing mighty works, but in their love of Jesus and the truth.  If people show these in their lives, we can conclude that they have God as their Father, but not otherwise.