Short answers, pulled from the story.
The Conseil d'Etat is a French governmental body that serves simultaneously as the supreme administrative court and as the principal legal adviser to the executive branch. It reviews government orders and draft legislation before they take effect and hears appeals against national administrative decisions, with its rulings being final and unappealable.
The current Conseil d'Etat was established in 1799 by the French Consulate government, with Napoleon presiding over its sessions as First Consul. Its origins trace further back to a council officially established in 1557 under the French monarchy, itself descended from the King's Council of the 13th century.
The Conseil d'Etat is located in the Palais-Royal in Paris.
The Vice President of the Council of State holds the real day-to-day presidency and presides over all but the most ceremonial assemblies. The Vice President is appointed by Order-in-Council on the recommendation of the Minister of Justice and ranks as the ninth most important civil servant in France.
The Conseil d'Etat recruits mainly from the top-ranking graduates of the Ecole nationale d'administration, France's training institution for senior civil servants. Members belong to a Grand Corps of the French State, a classification reserved for the highest levels of the national administration.
GAJA stands for Les Grands Arrets de la Jurisprudence Administrative and is a publication by Dalloz editions that collects the most important rulings of the Conseil d'Etat. It explains approximately 120 rulings from 1873 to the present and is written by leading French legal scholars including Bruno Genevois and Prosper Weil.