Short answers, pulled from the story.
The Paris Symphony received its private premiere on the 12th of June 1778 at the home of Count Karl Heinrich Joseph von Sickingen in Paris. The public premiere followed six days later at the Concert Spirituel.
Mozart composed Symphony No. 31 in D major, K. 297/300a, during a stay in Paris in 1778 when he was 22 years old and seeking employment. It was written for Joseph Legros, director of the Concert Spirituel, and premiered there, giving it the name Paris Symphony.
Yes. Symphony No. 31 was Mozart's first symphony to include clarinets. The score calls for two clarinets in A alongside two flutes, two oboes, two bassoons, two horns, two trumpets, timpani, and strings.
The original slow movement was an Andantino in 6/8, which, according to Otto Erich Deutsch, "had failed to please." Mozart replaced it with a new Andante for a Concert Spirituel performance on the 15th of August 1778. Both movements survive, along with a sketch of an earlier version of the Andantino.
Jean-Georges Sieber published the symphony in Paris, announced for sale on the 20th of February 1779. It may have been the first of Mozart's symphonies to appear in print. Sieber's catalog listed it as part of the Concert Spirituel repertoire from 1782 to 1788.
The autograph manuscript of Symphony No. 31, along with the manuscript of the alternative middle movement, is preserved in the Berlin State Library.