Short answers, pulled from the story.
Wolfgang Amadeus Mozart received a commission for Idomeneo in 1780 from Karl Theodor, Elector of Bavaria. He completed the work during that year to serve as a new opera for the court carnival season.
Idomeneo premiered on the 29th of January 1781 at the Cuvilliés Theatre in Munich. Christian Cannabich served as musical director for that first performance which ran three times during its initial engagement.
Richard Strauss created an adaptation of Idomeneo in 1931 for Vienna State Opera performances by replacing approximately one-third of Mozart's original score with his own compositions. He introduced motifs from Die ägyptische Helena into the new arrangement and rewrote Idamante specifically as a tenor role rather than castrato.
Boris Goldovsky produced the first United States performance of Idomeneo at Tanglewood during summer 1947. Glyndebourne Festival presented multiple acclaimed productions starting in the 1950s to bring historical awareness back to the stage.
The librettist Giambattista Varesco adapted the text from a French play by Antoine Danchet. Danchet had based his story on a 1705 tragedy by Crébillion père while André Campra had previously set this same story to music as Idoménée in 1712.