Short answers, pulled from the story.
Mozart completed Symphony No. 41 in C major, K. 551, on the 10th of August 1788. It was the last of three symphonies he wrote in rapid succession that summer, following No. 39 on the 26th of June and No. 40 on the 25th of July.
The nickname Jupiter is most commonly attributed to the impresario Johann Peter Salomon, who had settled in London around 1781. A second attribution names Johann Baptist Cramer, an English music publisher, who reportedly associated the symphony's opening chords with Jupiter and his thunderbolts.
It is not known with certainty whether the Jupiter Symphony was performed during Mozart's lifetime. A performance at the Gewandhaus in Leipzig in 1789 is documented in a concert programme. Mozart was preparing a series of concerts in Vienna at the time of composition, but historians have not confirmed whether those concerts took place.
The finale, marked Molto allegro, introduces five themes and then combines them simultaneously in a fugato passage at the movement's close. Sir George Grove called it the passage where Mozart reserved "all the resources of his science" and described the symphony as "the greatest orchestral work of the world which preceded the French Revolution."
The four-note theme (C, D, F, E) that anchors the finale is a common plainchant motif traceable to at least Thomas Aquinas's "Pange lingua gloriosi corporis mysterium" from the 13th century. Mozart used it throughout his career, including in his Symphony No. 1 in 1764 and in the Credo of an early Missa Brevis in F major.
The oldest known recording dates to around the beginning of World War I, issued by the Victor Talking Machine Company in its black label series. The performers were listed as the Victor Concert Orchestra, with conductor Walter B. Rogers identified only in company ledgers. The first movement was recorded on the 5th of August 1913.