God is absolutely responsible for Satan's actions, and for all of our actions as well. And at the same time, Satan is responsible for his own actions and we are responsible for ours. Free will and predestination are both true.
How is this possible? In the same way that quantum physics and classical physics can seamlessly coexist, that light can have both a particle and a wave nature, that causes and effects can be deterministic at the macro level and yet probabilistic at the micro level... Merely regarding the natural world, the scientist J.B.S. Haldane said, "The Universe is not only queerer than we suppose, but queerer than we can suppose." How much more, then, the Creator of the whole of nature?