Short answers, pulled from the story.
The Inquisition began as a judicial procedure in the 12th century, specifically transforming the Church into a legal prosecutor after Pope Lucius III issued the bull Ad Abolendam on the 11th of November 1184. This shift occurred as a response to the spread of Catharism and Waldensianism in southern France, replacing earlier methods like excommunication with formal tribunals.
Notable inquisitors included Robert of Auvergne who burned 183 Cathars in Montwimer on the 13th of May 1239, and Konrad of Marburg who operated in the Rhineland and Thuringia between 1231 and 1233. In Italy, Ruggiero burned at least 11 people in Tuscany between 1244 and 1245, while the Spanish Inquisition was led by Tomás de Torquemada as the first Grand Inquisitor starting in 1478.
The Spanish Inquisition was established in 1478 by King Ferdinand II of Aragon and Queen Isabella I of Castile, and it was formally ended by proclamation on the 15th of July 1834. Records studied by historians Gustav Henningsen and Jaime Contreras list 44,674 cases with 826 resulting in executions in person and 778 in effigy, while William Monter estimated 1,000 executions in Spain between 1530 and 1630.
The bull Ad extirpanda of 1252 authorized non-bloody torture methods such as the Strappado, the Rack, and the Water cure, which involved pouring water into a prisoner's mouth to simulate drowning. Instruments like the Iron Maiden, the Pear of Anguish, and the Spanish Boot were never used by the Inquisition but were erroneously registered in museums by later pranksters and con artists.
The Portuguese Inquisition formally started in Portugal in 1536 at the request of King João III, with the first auto-da-fé held in 1540. It principally focused upon Sephardi Jews from Spain who had fled or been forced to convert to Christianity, resulting in the burning of 1,175 persons and the penancing of 29,590 between 1540 and 1794.
The Roman Inquisition tried Galileo Galilei in 1633, and its proceedings involved public ceremonies known as the sermo generalis or auto-da-fé to pronounce sentences. Following the French invasion of 1798, new authorities sent 3,000 chests containing over 100,000 Inquisition documents to France from Rome, and the institution now survives as part of the Dicastery for the Doctrine of the Faith.