Short answers, pulled from the story.
Joseph Leutgeb was a horn player of the classical era, born on the 6th of October 1732 and died on the 27th of February 1811 in Vienna. He was a close friend and musical inspiration to both Joseph Haydn and Wolfgang Amadeus Mozart.
Mozart wrote the Horn Concertos K. 417, K. 495, and K. 412/386b (also numbered 514) for Joseph Leutgeb, and probably the Horn Quintet K. 407/386c. These works date from after 1781, once Mozart had settled in Vienna, and the concertos remain central to the solo horn repertoire today.
No, Joseph Leutgeb never ran a cheese shop. The business was actually a sausage shop belonging to his father-in-law, a Cerveladmacher who produced Italian style sausages until his death in 1763, and the shop was sold in 1764.
Joseph Leutgeb joined the Prince-Archbishop's musical establishment in Salzburg in 1763, working alongside Leopold Mozart. There he became friends with Leopold's seven-year-old son Wolfgang, who later listed Leutgeb among the people he missed while touring in a letter dated the 20th of August 1763.
Mozart added joking, mocking comments to the horn parts he wrote for Joseph Leutgeb as part of a close, teasing friendship. On the score of K. 417, dated the 27th of March 1783 in Vienna, Mozart wrote a mock dedication calling him an ass, an ox, and a simpleton.
Joseph Leutgeb played the natural horn, which had no valves, since the valve was not invented until after 1814 by Heinrich Stölzel and patented in 1818. He relied on precise lip control and a hand-stopping technique to reach chromatic notes.