Short answers, pulled from the story.
The manuscript bears the date the 5th of January 1791. Paper analysis by musicologist Alan Tyson reveals the sheet music paper was used between December 1788 and February 1789.
Historical records point to a concert held in Jahn's Hall where Mozart himself may have played alongside clarinetist Joseph Beer. An alternative scenario involves his pupil Barbara Ployer premiering the work at the Palais Auersperg in January 1791.
Mozart scored this piece with flute, two oboes, two bassoons, and two horns in B-flat. The solo piano part sits atop strings without trumpets or timpani.
All three movements reside in a major key yet suggest minor tonalities through specific thematic choices. A remote minor key emerges during the early development section while the tonic minor key surfaces in the middle of the Larghetto movement.
The principal theme reappears in a later song composition by Mozart cataloged as K. 596 titled Sehnsucht nach dem Frühling. This melody serves as the basis for that song which follows the concerto immediately in the Köchel catalogue sequence.