Short answers, pulled from the story.
Shakespeare wrote Othello around 1603. The play's terminus ad quem is 1604, when a performance is recorded in the accounts of Sir Edmund Tilney, then Master of the Revels. The earliest possible date is 1601, when one of Shakespeare's key sources, Philemon Holland's translation of Pliny's Natural History, was published.
Shakespeare's primary source was a novella by the Italian author Cinthio (Giovanni Battista Giraldi), from a collection called Gli Hecatommithi, published in 1565. The story appears in the third decade of the collection, which deals with marital infidelity. Shakespeare substantially reworked the plot, adding the Turkish military threat and altering the manner of Desdemona's death.
Othello was first published in a quarto edition in 1622, followed a year later by its appearance in the First Folio of 1623. The two texts differ significantly: the Folio contains about 160 lines not in the quarto, while the quarto has fuller stage directions and 63 oaths or profanities absent from the Folio. Scholars have never reached consensus on which text has greater authority.
The first known professional performance of the title role by a black actor was James Hewlett at the African Grove Theatre in New York in 1822. His protege Ira Aldridge, billed as 'The African Roscius,' subsequently played the role at the Royalty Theatre in London in 1825 and continued performing Shakespearean roles across Europe for forty years.
The handkerchief is the first gift Othello gave Desdemona and the central piece of false evidence Iago uses to convince Othello of her infidelity. Critics since Thomas Rymer in 1693 have noted how much of the play's catastrophe depends on this single prop. The play deliberately contradicts itself about the handkerchief's origins, with Othello attributing it at different moments to an Egyptian charmer and to his own father.
Shakespeare never provides Iago with a single clear motive; the character expresses multiple contradictory ones, including resentment over Cassio's promotion, racial hatred of Othello, suspicion that Othello slept with his wife Emilia, suspicion that Cassio did the same, and his own love for Desdemona. Samuel Taylor Coleridge called this the "motive-hunting of motive-less Malignity." At the play's end, Iago refuses to explain himself, vowing permanent silence.