Short answers, pulled from the story.
Maximilian III Joseph (the 28th of March 1727 - the 30th of December 1777) was a Prince-elector of the Holy Roman Empire and Duke of Bavaria from 1745 to 1777. He was the last of the Bavarian branch of the House of Wittelsbach and was known by the epithet "the much beloved."
The War of the Bavarian Succession broke out because Maximilian III Joseph died on the 30th of December 1777 without leaving an heir. Austria immediately invaded portions of the duchy, and his 12th cousin once removed, Elector Palatine Charles Theodore, inherited a realm he had no interest in ruling.
The Treaty of Fuessen was a peace agreement Maximilian signed with Habsburg empress Maria Theresa following the decisive defeat of Bavarian forces at the Battle of Pfaffenhofen on the 15th of April 1745. The 18-year-old elector agreed to support Maria Theresa's husband in the upcoming imperial election in exchange for peace, abandoning his father Emperor Charles VII's imperial ambitions.
Maximilian III Joseph founded the Bavarian Academy of Sciences in 1759, Munich's first academic institution, and in 1770 established the precursor of the Academy of Fine Arts, Munich. He also oversaw the establishment of the Nymphenburg Porcelain Factory in 1747 and the introduction of general school attendance regulation in 1771.
Maximilian III Joseph received Mozart at his court but could not offer him a position due to strict frugality. Despite this, Mozart's Italian opera La finta giardiniera received its world premiere at the Salvatortheater in Munich in 1775 during Maximilian's reign.
Maximilian III Joseph died on the 30th of December 1777 from a virulent strain of smallpox known at the time as "purple small pox." He fell ill shortly after riding through Munich in December 1777; none of his 15 doctors could initially diagnose the disease, but by Christmas the illness had become clear.