Short answers, pulled from the story.
The Knights Templar, formally the Poor Fellow-Soldiers of Christ and of the Temple of Solomon, were a military order of the Catholic faith founded in 1118 to defend pilgrims traveling to Jerusalem. They were headquartered on the Temple Mount and existed for nearly two centuries during the Middle Ages.
King Philip IV was already deeply in debt to the Templars from his war against England and seized on rumours against the order to free himself from those debts. At dawn on Friday, the 13th of October 1307, he had Grand Master Jacques de Molay and scores of other French Templars arrested simultaneously.
Jacques de Molay, the last Templar Grand Master, was burned at the stake in Paris on the 18th of March 1314 after he retracted a confession given under torture and was declared a relapsed heretic. From the flames he reportedly warned that Pope Clement V and King Philip IV would soon meet him before God, and both men died within the same year.
Beginning in 1150, the Knights Templar issued letters of credit so pilgrims could deposit valuables at a local preceptory, receive a document recording the value, and claim treasure of equal worth on arrival in the Holy Land. This arrangement protected pilgrims from robbery and may have been the first use of bank cheques.
Pope Clement V disbanded the Knights Templar in 1312 at the Council of Vienne through the bull Vox in excelso, citing the public scandal generated by confessions extracted under torture. He acted under pressure from King Philip IV, and most Templar assets were transferred to the Knights Hospitaller through the bull Ad providam.
After the Templars were dissolved, the Order of Christ was created in Portugal in 1319 under King Denis I, who refused to persecute the former knights and absorbed many of them along with their properties. The Order of Christ, headquartered at the former Templar castle in Tomar, is considered a successor to the Knights Templar.
The Chinon Parchment, dated the 17th to the 20th of August 1308, is a record of the Templar trial discovered in the Vatican Archives in September 2001 by Barbara Frale. It shows that Pope Clement V absolved the Templars of all heresies in 1308, before he formally disbanded the order in 1312.