Some contemporary scholars think the destruction of Troy VIIa circa BC was the origin of the myth of the Trojan War, others that the poem was inspired by multiple similar sieges that took place over the centuries.
In addition, Aristotle described him as a unique poet of his time in his work, Poetic. Since then the proliferation of translations has helped to make them the most important poems of the Classical European tradition.
Homer's death is less controversial, Ios being the overwhelming favorite.
The Odyssey tells the story of Odysseus and his journey after the end of the Trojan War. The story highlights Achilles' bravery and the glorification of war. Scholars are uncertain whether he existed. There were plenty of other writers of what is called the "epic cycle" who contributed details not found in Homer.
Since it's not even clear that Homer lived, and since we don't have a fix on the location, it should come as no surprise that we don't know when he was born.