Ok, but, if it is so that Jesus is in us all, is it not also, of necessity, that Satan, too, is in us all and that that, winning the internal battle, is the goal of the faith?
Uh, no, I think you are wrong on all accounts there. Quick summary:
G-d is in all of us. We have to choose to accept Jesus. We have to choose to accept G-d. We have free will / free choice.
The devil is not G-d or even a g-d. He was a cherub, an angel, a servant of G-d who had free choice and he chose poorly. With his downfall, he ushered in original sin.
Read Ezekiel to learn more.
I'm excerpting the following from
http://www.religionfacts.com/the_devil.htm because it sums up much better than I could what the devil does.
Presently, Satan works in different ways against the believer and the unbeliever, according to the Bible. With regard to unbelievers, he blinds their minds to the person of Jesus Christ, according to the Apostle Paul (e.g. 2 Cor. 2:3-4), blocks the truth from their hearts (e.g. Matt. 13:4), promotes false religion (e.g. 2 Cor. 11:13-15), and ushers evil into the human heart (e.g. John 13:2). With regard to believers he seeks to promote disruptive attitudes and actions (e.g. 2 Cor. 2:10-11), distort a person's view of Jesus Christ (e.g. 2 Cor. 11:2-3), tempt toward immorality (e.g. 1 Cor. 7:5), and makes accusations against believers (e.g. Rev. 12:10).