Short answers, pulled from the story.
German-occupied Europe peaked in 1941-1942, when Germany and Italy together controlled more than half of the entire continent's population through direct administration, civil occupation, military occupation, and puppet states.
Roughly 1.65 million people were registered as prisoners across the camp system, of whom approximately a million died during their imprisonment. Most fatalities occurred during the second half of World War II, and at least 4.7 million Soviet prisoners had been registered by January 1945.
The first concentration camps opened in March 1933, immediately after Adolf Hitler became Chancellor of Germany. After the 1934 purge of the SA, the camps were placed under exclusive SS control.
Many occupied nations formed governments-in-exile, including Poland, France, Norway, Belgium, the Netherlands, Czechoslovakia, Greece, Yugoslavia, and Luxembourg. The Polish government-in-exile operated from Paris, then Angers, then London from the 12th of June 1940, and persisted until December 1990.
At its farthest extent, the Wehrmacht occupied territory as far north as Franz Josef Land in the Soviet Union, as far south as Gavdos in Greece, and as far west as Ushant in France.
Allied forces gradually liberated the camps in 1944 and 1945, but hundreds of thousands of prisoners died in death marches that the SS ordered as Allied forces advanced. Some camps, including Auschwitz, held prisoners from many different nationalities transferred from across occupied Europe.