Short answers, pulled from the story.
Mozart completed the Prague Symphony, K. 504, on the 6th of December 1786, according to his own autograph thematic catalogue. It premiered in Prague on the 19th of January 1787, during Mozart's first visit to the city.
The symphony is called the Prague Symphony because it received its premiere performance in Prague on the 19th of January 1787. It was not performed in Vienna before that Prague debut.
No definitive explanation has been established. Alan Tyson conjectured that Mozart ran out of time when assembling the work. Daniel E. Freeman proposed that the three-movement format was a deliberate choice to appeal to Prague audiences, whose favored composer Josef Mysliveček wrote almost exclusively in the Italian three-movement pattern.
By analysing paper types in Mozart's autograph, Alan Tyson found that the third movement was composed first, on paper matching Mozart's earlier work on Le nozze di Figaro. The first and second movements were written on paper corresponding to late 1786, suggesting the symphony was assembled in reverse order.
The overwhelming success of Le nozze di Figaro during its run at the National Theatre in Prague during the 1786-87 winter season led a group of musicians and patrons to invite Mozart to the city, as recorded in a letter by Leopold Mozart written in January 1787.
The symphony's advanced use of wind instruments, including extended passages where no strings play at all, was continued in Mozart's own final symphonies and was later adopted in the London symphonies of Haydn, and in works by Beethoven and Schubert.