Fortunately, the Bible stands up accurate vs. human opinions. We are living in the times of Revelation, are we not?
At Rev 12:11-12 it says that Satan and those who rebelled with him were kicked out of heaven and "Woe to the earth and to the sea..." Earlier, in the chapter it's talking about this event happening because of Christ's sacrifice (blood of the Lamb) and when he assumes the throne.
Where, do the scriptures separate Satan as something different from spirit? Eph 2:2 uses the word air and spirit in the same way we would use the word "spirit" in "School Spirit"...It's a word to say: the mindset, influence, ideals expressed by of the given source. By that I mean, if we are moved by our loyal love of God to DO what is right as we are instructed to in the Bible, then we are exressing God's spirit (not speaking of Holy Spirit, but rather personality) the way Christ did. Yet, If we are expressing the spirit/air of the "world" it looks like this: putting our wants before what God wants, quick anger, always ready for conflict, talk the talk but not walk the walk, dishonest, sexual misconduct (meaning ALL sexual behavior contrary to Bible standards), being a part of wild partying (revelries)...That is the spirit of Satan, not something that exists aside from him.
The world reveals that the dominating personality of humans reflects the air (personality) of Satan.
Satan's children are any that reflect his spirit. Most call themselves some sort of religion, Christian, Muslim, Hindu, Jew, but the air of Satan is what is evident in their lives...even their private lives are visible to God. Therefore, we must always, EVERY DAY keep proving our allegiance to God's rule by reflecting his values, his personality.
The challenge is to be a law abiding citizen in a land of sin.