Short answers, pulled from the story.
The Importance of Being Earnest had its world premiere on the 14th of February 1895 at the St James's Theatre in London. The opening night was Valentine's Day, and the play was preceded by a short curtain-raiser called In the Season by Langdon E. Mitchell.
The play closed on the 8th of May 1895 after 83 performances because of Oscar Wilde's arrest and conviction for gross indecency. Wilde's prosecution stemmed from his feud with the Marquess of Queensberry, whose son Lord Alfred Douglas was Wilde's lover. Box-office receipts collapsed after Wilde's arrest, and George Alexander removed the author's name from the playbills in an unsuccessful attempt to save the run.
Wilde scholars broadly agree that the most important influence on the play was Gilbert's 1877 farce Engaged. Wilde borrowed several incidents from it and, as Russell Jackson wrote in his 1980 introduction, adopted "the gravity of tone demanded by Gilbert of his actors", applying deadpan seriousness to outright absurdity.
Edith Evans played Lady Bracknell in John Gielgud's celebrated 1939 production and again in the 1952 Anthony Asquith film. Judi Dench took the role in Peter Hall's 1982 National Theatre production and in a 1995 Radio 4 centenary broadcast. Men have also played the part: Geoffrey Rush for the Melbourne Theatre Company in 2011, Brian Bedford on Broadway in 2011, David Suchet at the Vaudeville Theatre in 2015, and Stephen Fry in the National Theatre's 2025 transfer to the Noel Coward Theatre.
The play has been adapted for cinema three times. Anthony Asquith directed the first film version in 1952 with Michael Redgrave and Edith Evans. Kurt Baker directed a 1992 version using an all-black cast set in the United States. Oliver Parker directed a 2002 version starring Colin Firth, Rupert Everett, and Judi Dench.
In the play, Bunburying refers to Algernon Moncrieff's practice of inventing a sickly friend named Bunbury in the country, whom he can claim to visit whenever he wants to escape an unwelcome social obligation. Bunbury is a real village in Cheshire. Theories about Wilde's choice of the name include a hypochondriacal acquaintance of his youth named Henry Shirley Bunbury and names Wilde reportedly encountered in The Worthing Gazette in August and September 1894.