Short answers, pulled from the story.
The earliest recorded performance of The Comedy of Errors took place on the 28th of December 1594, in Gray's Inn Hall, London, described in the Gesta Grayorum as a performance by a company of base and common fellows during the inn's revels. A second performance occurred on the same date ten years later, the 28th of December 1604, at Court.
The Comedy of Errors is a modernised adaptation of the Roman comedy Menaechmi by Plautus, supplemented by elements from Plautus's Amphitryon. Shakespeare doubled the single pair of twins in Menaechmi to create two pairs: the Antipholus brothers and the Dromio brothers.
Scholar Charles Whitworth argues it was written in the latter part of 1594, based on historical records and its textual similarities to other plays Shakespeare wrote around that time. The play contains a reference to the wars of succession in France, placing it somewhere between 1589 and 1595.
Two sets of identical twins, Antipholus of Syracuse and Antipholus of Ephesus and their servants the two Dromios, unknowingly converge on Ephesus, triggering a day of mistaken identities that leads to wrongful beatings, an arrest, accusations of theft, madness, and demonic possession. The confusion is resolved when an Abbess reveals herself to be Emilia, the long-lost wife of Aegeon, reuniting both twin pairs and their family.
The most famous musical adaptation is The Boys from Syracuse, with music by Richard Rodgers and lyrics by Lorenz Hart, which premiered on Broadway in 1938 and was made into a film in 1940. The Royal Shakespeare Company's 1976 musical version, with book and lyrics by Trevor Nunn and music by Guy Woolfenden, won the Laurence Olivier Award for best musical in 1977.
Gli equivoci, composed by Stephen Storace with a libretto by Lorenzo da Ponte, premiered at the Burgtheater in Vienna on the 27th of December 1786. Da Ponte, who also wrote librettos for Mozart, based the text on a French translation of Shakespeare's play, cutting the characters of Aegeon and Emilia.