If satan does not have a physical body, and cannot operate within the mind, what power does he have? As I see it, that is the only way they have power at all. Teaching people with open minds all kinds of doctrine of demons.

I believe satan and the demons are handicapped by their inability to see the future. As we know the ability to predict the future is God's alone. That is how God can work all things together for good, despite Satan working hard to mess things up. Take the holocaust for example. Was the hatred of Jews influenced by satan? Absolutely. It was satan trying to throw a wrench into God's plan, by trying to eliminate the Jews. However, as we saw, God used it for good.