Since the first duke of England was the Duke of Cornwall, the son of Edward III, 1337, I'm going to assume that the first Duchy would be the same, Duchy of Cornwall. The Duchy of Lancaster is held by the Soverign. in Lancaster the toast, "To the Queen, Duke of Lancaster" that's "Duke" not Duchess.
An archipelago is a cluster or a string of islands. The one that has the greatest number of islands in it is the Archipelago Sea, which belongs to Finland. The archipelago with the greatest land area is Indonesia.