Short answers, pulled from the story.
Wolfgang Amadeus Mozart composed the motet Exsultate, jubilate in 1773 while staying in Milan. The work emerged during the production of his opera Lucio Silla at the Teatro Regio Ducale.
The first performance took place inside the Theatine Church on the 17th of January 1773 with Venanzio Rauzzini singing the solo part. Rauzzini sang the role even while performing in Mozart's opera later that same night.
The opening movement is titled Exsultate jubilate and moves at an Allegro pace in F major. A secco recitative follows under the heading Fulget amica dies, followed by Tu virginum corona as an Andante in A major. The final movement returns to Allegro speed in F major under the label Alleluja.
On the 30th of May 1779, a Trinity Sunday, a revised version appeared at the Holy Trinity Church in Salzburg. Francesco Ceccarelli performed that altered edition before a local congregation.
A 1990 CD and DVD recording features Arleen Auger with the Bavarian Radio Symphony Orchestra under Leonard Bernstein. This release captures the piece using modern orchestral forces rather than period instruments.