Short answers, pulled from the story.
Isengard comes from Old English ísen, meaning "iron", and geard, meaning "court" or "enclosure". In Tolkien's elvish language Sindarin, the same fortress was called Angrenost, a compound carrying the same meaning of an iron enclosure.
The Númenóreans in exile built Isengard during the Second Age as a walled circular enclosure. The tower at its centre, Orthanc, was constructed toward the end of the Second Age by men of Gondor from four many-sided columns of rock joined by an unknown process.
Saruman was given the keys to Orthanc by the Steward of Gondor, Beren, when he reappeared from the East and offered to guard the fortress. He first resided there as Warden of the Tower on behalf of Gondor, then declared himself Lord of Isengard on Sauron's return to Mordor.
Treebeard, leader of the Ents, led an army of Ents and Huorns to Isengard, destroyed it, and flooded it after the Orcs of Isengard attacked the forest of Fangorn. The Ents could not break the tower of Orthanc, which remained standing in the wreckage.
Tom Shippey draws the comparison because the Mouth of Sauron's proposed settlement after Gondor's surrender mirrors the 1940 Vichy treaty: a demilitarized zone west of the Anduin that would pay war-reparations and be governed from Isengard by what Shippey calls "a Quisling". The promised governor of Isengard is explicitly described as Sauron's lieutenant, not a sovereign.
Tolkien states in The Two Towers that Orthanc has two meanings: "Mount Fang" in Sindarin, and "Cunning Mind" in the Old English he used to represent Rohirric. The English scholar Clark Hall confirms that the Old English orþanc genuinely means "intelligence, understanding, mind; cleverness, skill".