Short answers, pulled from the story.
The Trojan Horse was a massive wooden horse built by the Greeks during the Trojan War at the suggestion of Odysseus. An elite force of warriors hid inside, and the Trojans were deceived into pulling the structure inside their city as a trophy. That night the hidden soldiers emerged, opened the gates for the returning Greek fleet, and destroyed Troy.
No. The Trojan Horse does not appear in Homer's Iliad, which ends before the war concludes. It is mentioned only briefly in the Odyssey, composed around the 8th century BC. The most detailed ancient account comes from Virgil's Aeneid, written around 19 BC.
Two figures warned the Trojans. The priest Laocoön guessed the plot and declared "I fear Greeks, even those bearing gifts," but Poseidon sent two sea serpents to kill him and his sons Antiphantes and Thymbraeus before anyone listened. King Priam's daughter Cassandra also predicted the horse would destroy the city and the royal family, but she too was ignored.
Ancient sources give conflicting numbers. One tradition places 30 warriors in the horse's body with 2 spies in its mouth. The Bibliotheca gives 50, Tzetzes gives 23, and by late tradition the number was standardized at 40. Odysseus led the group inside, which included Diomedes, Menelaus, Neoptolemus, and Ajax the Lesser.
The earliest surviving depiction of the Trojan Horse is on a Boeotian fibula dated to around 700 BC. Two relief storage jars from the Greek islands of Mykonos and Tinos, dated between 675 and 650 BC, provide more detailed images. Historian Michael Wood dates the Mykonos vase to the 8th century BC, before the written accounts attributed to Homer.
No archaeological evidence confirms a literal wooden horse. Scholars have proposed several factual explanations: the horse may have been a siege engine, since animal names were commonly given to ancient military machinery; it may have been a Phoenician merchant ship decorated with a horse's head, called hippos by Greeks; or Fritz Schachermeyr proposed it was a metaphor for an earthquake, since archaeological digs have confirmed Troy VI suffered major earthquake damage.