What to do about my neighbour who is evil?

There are many who are not well balanced to begin with, and many who latch onto the ravings of some hysterical preacher as if their messages were the literal truth. This woman sounds as though she had her brain fried years ago and has 'connected' with God, via some fire and brimstone evangelist. I would contact the social services agency nearest your home, explain the problems to them and ask them for an intervention. If nothing else, perhaps they can get a magistrate to issue a 'no contact' writ. If one can be obtained and she then violates it, you'll have the right to have the police become involved.