Omnipotent means all powerful. You mean omnipresent. So if you are wrong there the rest of your assumptions are not valid. Satan is different and separate from God. as he was a created being and the highest ranking angel.
From what I hear, God and Satan are two separate beings. I think God is just part of every person while Satan is just part of every demon (for the most part.) Personally I sometimes imagine God and Satan being aliens who created all life on Earth or in the Solar System in general by means of natural phenomena. People say that life on Earth during the time of Theia's destruction is impossible since the planet was too hot and melted for life to even exist at that point, but how do we know the whole planet was molten lava?
2) is incorrect. You have confused "omnipotent" with "omnipresent".
3) Being co-extensive with all things is not the same as being identical with all things, which would be a specific theological position called "pantheism". And "apart" written as one word actually means the opposite of what you want it to mean.
So 4) and 5) cannot be validly surmised from your premise. However, it's certainly the case that in standard Christian theology, all creation is contingent on God's sustaining will; and Satan is a created being. Therefore, it's correct to say that Satan only exists because God wills it so.