Short answers, pulled from the story.
Vichy France was officially established on the 10th of July 1940, when the French National Assembly voted by 569 votes to 80 to grant full powers to Marshal Philippe Pétain. It lasted until the 9th of August 1944, when the Provisional Government issued an ordinance restoring republican government to France.
The government chose Vichy as its seat because it was centrally located in unoccupied southern France, had large hotels to house administrative offices, and had reliable telephone and telegraph connections. Lyon was considered too associated with socialists, Marseille had a reputation for organized crime, and Bordeaux was a port subject to direct German military administration.
At least 72,500 Jews deported from Vichy France were killed in Nazi concentration camps. Of these, about 24,000 were Jews of French origin, with the majority being foreign-born.
No. Despite heavy pressure from Germany, the Vichy government never formally joined the Axis powers. France was officially declared a neutral country under the armistice terms, though it pursued a policy of collaboration with Germany.
The Révolution nationale was the official ideological programme of the Vichy regime. It called for an authoritarian counter-revolution against the liberal traditions of the French Republic, blamed France's defeat on alleged moral decay and political liberalism, and promoted traditional values of rural life, hierarchy, and Catholic faith. The national motto Liberty, Equality, Brotherhood was replaced with Work, Family, Homeland.
Germany held approximately two million French soldiers as prisoners of war. About a third had been released on various terms by 1944. By 1945, nearly half a million French prisoners were still living on German soil.