What was the German monarchy, and how was it related to Prussia and Nazism?
Prussia was one of the three hundred principalities that comprised what is now Germany. It and Austria were the two leading principalities. Otto von Bismarck, later Chancellor of the united Germany, was largely responsible for uniting Germany under Prussian leadership. He did this by a series of wars against Austria and France, the end result of which was not only the cession of territory to Germany but also a sharp increase in German nationalism. Part of Bismarck's plan was to exclude Austria from the united Germany, as Austria would have been a rival to Prussia for domination of the Empire. Following the Franco-Prussian War in which France was humiliated, Bismarck arranged for King Wilhelm 1 of Prussia to be crowned Kaiser (the German equivalent of Caesar) of Germany.There were only two Kaisers of the German Empire, Wilhelm I and II. The family name ("House") was Hohenzollern.
The success of the Franco-Prussian war left Germans somewhat drunk with success and prone to a Social Darwinist way of thinking. They considered themselves the fittest and best of the European species. They also embraced a new authoritarian conservatism based on nationalism.
Any connection with Hitler is indirect at best. Hitler did appeal to German nationalism and socialism and promoted the idea of the Germans as superior to all others. The German Empire under Wilhelm I and II had been, in Hitler's vision, the Second Reich. (The First Reich had been the Holy Roman Empire which comprised most of present day Germany.) Hitler built on this by calling his regime the Third Reich.