Short answers, pulled from the story.
Thomas North published his translation of Plutarch's Lives in 1579. Shakespeare mined that volume for the bones of Coriolanus and borrowed heavily from the Life of Caius Martius Coriolanus found within those pages.
Most scholars place the composition of Coriolanus between 1605 and 1610, with late 1608 to early 1609 being the most likely window. The earliest date rests on Menenius's belly fable derived from Camden's book published in 1605.
Caius Marcius received an official nickname after he fought Tullus Aufidius until Aufidius's soldiers dragged him away from their single combat while forcing open the gates of the Volscian city of Corioli alone. Cominius named him Coriolanus after this feat to define his public identity.
T.S. Eliot proclaimed Coriolanus superior to Hamlet in The Sacred Wood calling it one of the Bard's greatest tragic achievements alongside Antony and Cleopatra. A.C. Bradley described this play as built on the grand scale like King Lear and Macbeth yet differing in important ways.
No recorded performance exists prior to the Restoration period after 1660. Nahum Tate presented a bloody adaptation at Drury Lane in 1682 that remained faithful through four acts before becoming a Websterian bloodbath in the fifth act.