Short answers, pulled from the story.
Così fan tutte had its world premiere on the 26th of January 1790 at the Burgtheater in Vienna, Austria. Wolfgang Amadeus Mozart conducted at least one of the early performances himself, leading the second run of the June 1790 revival.
The libretto was written by Lorenzo Da Ponte, who also wrote the texts for Mozart's Le nozze di Figaro and Don Giovanni. Da Ponte had used the phrase "Così fan tutte le belle" in Le nozze di Figaro before Mozart and he gave it a full opera of its own.
The short title literally means "So do they all", using the Italian feminine plural tutte to indicate women. It is often translated as "Women are like that". The phrase is sung by the three male characters in act 2, scene 3, and is also quoted in the opera's overture.
Nineteenth and early twentieth-century audiences considered the opera's subject matter risqué, vulgar, and even immoral. When it was performed, it typically appeared in bowdlerised versions with the plot altered. The opera did not reclaim a regular place in the standard repertoire until after World War II.
The United States premiere of Così fan tutte took place in 1922 at the Metropolitan Opera. Britain had seen the work earlier, with the first British performance given at the King's Theatre in London in May 1811.
According to William Mann, Mozart wrote "Come scoglio" specifically to exploit the awkward habits of the original Fiordiligi, soprano Adriana Ferrarese del Bene. Knowing she dropped her chin on low notes and threw her head back on high ones, Mozart packed the aria with constant leaps between low and high registers, with the intent of making her head bob conspicuously on stage.