Is God “Divided Against Himself” When He Allows Evil?

Questions about whether the principle that a house divided against itself can’t stand would apply not only to Satan casting out demons but also to God allowing evil, whether or not God is the author of everything he permits for a purpose, and the primary sin of Eve.  

• Wouldn’t the principle in Mark 3:24–25 that a house divided against itself can’t stand apply not only to Satan casting out demons but also to God allowing evil?
• If God is pleased, according to his wise and holy counsel, to permit something, having purposed it to his own glory, does that make him the author of that which he purposed?
• What was the primary sin of Eve? Was it coveting? Pride? Curiosity?