Short answers, pulled from the story.
The concerto is nicknamed "Lodron" because it was commissioned by Countess Lodron to be performed with her two daughters, Aloysia and Giuseppa. The family name attached to the piece through this commission and has remained its informal title.
Mozart originally wrote K. 242 for three solo pianos, two oboes, two horns, and strings. He later rearranged it for two pianos, and that version is the one most commonly performed today.
Mozart finished the original three-piano version in February 1776. He later revised it for two pianos in 1780 in Salzburg, apparently for himself and another pianist.
The first British performance was given on the 12th of September 1907 at Queen's Hall during the Proms. The three soloists were Henry Wood, York Bowen, and Frederick Kiddle, conducted by Henri Verbrugghen.
Musicologist C. M. Girdlestone identified a theme in the slow movement of K. 242 that reappears in more developed form in later concertos, particularly No. 25, K. 503. He discussed this in his book "Mozart and His Piano Concertos".
Mozart himself rearranged K. 242 from three pianos to two in 1780 in Salzburg, intending it for himself and one other pianist. That revised two-piano version became the standard performance version and is how the piece is most often heard today.