Short answers, pulled from the story.
Wolfgang Amadeus Mozart began writing dance music when he was five years old. His earliest efforts appear in the Nannerl Notenbuch, a manuscript book his father Leopold compiled for him and his sister Maria Anna.
The main obligation required him to compose dances for balls held in the public ballrooms of the Hofburg Imperial Palace. He complied with this requirement scrupulously by composing dances in great number each year between late December and early March during the carnival season.
Mozart's dances fall primarily into three distinct genres: minuet, German Dance, and contredanse. Minuets predominated early while later works favored the other two types which included lively German Dances and sequences from English country dance known as contredanses.
Mozart composed nine dances for full orchestra in full score by mealtime after being summoned an hour before dinner in early 1787. Nissen elsewhere relates another tale where Mozart composed four fully orchestrated contredanses in less than half an hour maintaining similar pace.
Wolfgang Amadeus Mozart included substantial ballet sequences at ends of several operas including Idomeneo premiered in 1781. He went against precedent writing ballet music himself rather than delegating it to another composer for works like The Marriage of Figaro from 1786 and Don Giovanni from 1787.