Dementia is a symptom of many different diseases. Alzheimer's is just one of the diseases that causes dementia.

In early Catholic tradition Jesus was believed to have died between 3:00pm and 4:00pm. The inversion of that, 3:00am and 4:00pm was called the "Devil's Hour". The "witching hour" is developed from that. Many cultures have other hours of early morning after midnight with similar superstitions. This is probably due in large part to the hours between midnight and 4:00am being the quietest time where almost all life, or life that we are accustomed to dealing with, is asleep. Indeed very few people ever are commonly awake at those hours. Societally, if you know that almost every single person in a village or city was asleep at those hours and if they're awake they are probably tired, that would make it the best time to do anything disagreeable like thieving, harming others, or anything else socially unacceptable like "witchcraft". You'd be a lot more likely to get away with it. Makes sense that someone in charge might like to keep people inside at those hours. Makes security a lot easier.