Short answers, pulled from the story.
Mendelssohn finished the overture, Op. 21, on the 6th of August 1826, when he was 17 years and 6 months old. He had been inspired by reading August Wilhelm Schlegel's German translation of Shakespeare's play that same year.
The overture premiered in Stettin, then in Prussia and now Szczecin, Poland, on the 20th of February 1827. The concert was conducted by Carl Loewe, and Mendelssohn had to travel 80 miles through a snowstorm to attend.
King Frederick William IV of Prussia commissioned the incidental music, Op. 61, after a successful staging of Sophocles' Antigone at the New Palace in Potsdam in 1841, for which Mendelssohn had also written music. The Midsummer Night's Dream production opened at Potsdam on the 14th of October 1843.
The Wedding March, which serves as the intermezzo between Acts 4 and 5, is described as probably the most popular single piece Mendelssohn ever composed and one of the most ubiquitous pieces of music ever written.
Thomas Attwood was given the score for safekeeping after the concert at the Argyll Rooms on the 24th of June 1829, but he left it in a cab and it was never recovered. Mendelssohn rewrote the entire overture from memory.
Rafael Frühbeck de Burgos recorded the complete incidental music with the New Philharmonia Orchestra and soloists Hanneke van Bork and Alfreda Hodgson for Decca Records in the 1970s. In October 1992, Seiji Ozawa and the Boston Symphony Orchestra recorded the full score for Deutsche Grammophon, with soloists Frederica von Stade and Kathleen Battle and actress Judi Dench reciting dialogue from the play.