Short answers, pulled from the story.
Paris was the shepherd boy who received a golden apple inscribed with the words for the fairest on Mount Ida. This event sparked a quarrel between three goddesses: Hera, Athena, and Aphrodite.
Homer composed two epic poems known as the Iliad and the Odyssey sometime between the ninth and sixth centuries BC. The Iliad covers only four days and two nights during the tenth year of the siege while the Odyssey follows Odysseus's ten-year journey home to Ithaca after the war ended.
Heinrich Schliemann met Frank Calvert in 1868 to discuss the location of ancient Troy at Hisarlık in modern-day Turkey. Excavations conducted by Schliemann and others confirmed this claim for most scholars today.
Scholars date the historical conflict to the twelfth or thirteenth century BC based on genealogies of kings. Eratosthenes proposed dates between 1194 and 1184 BC which roughly match archaeological evidence of a catastrophic burning of Troy VIIa.
Virgil wrote the Aeneid during the reign of Augustus to establish Roman national identity. This account introduced the Trojan Horse to Western literature though it does not appear in Homer's works.