Do Fascist governments exist?
Not really. Since WWII the word has been misused as a pejorative to describe governments which exercise authority in a way that you do not like. There are many authoritarian governments in the world today, but none fit the whole definition of fascism. Fascists believe that a nation must be ruled by a strong dictator. But they are defined more by what they oppose: Liberals, Democrats, Communists, Individualists and Racial minorities (esp. Jews). People use it to describe China (but it is run by a communist party – which is by definition anti-fascist), Fiji (which does not oppose racial minorities), Thailand (a kingdom), The USA (a liberal democracy), Zimbabwe (an authoritarian democracy), Syria (Baathist – hates Israel but is comprised of several racial groups notably Alawites), etc. but the label really fits only WWII Germany, Spain, Italy and their occupied territories.