Did the poet Homer actually exist or was the Iliad and the Odessey written by other writers?
He sang it more likely as much of literature was oral at that time and someone else wrote it down but on most editions of the Odyssey, it’s his name that is the author. Of course it’s translated for us by someone.
When you realize that the Iliad only covers a few weeks during the tenth year of the war and that the tradition of the people and events (Patroklus dies, Achilles dies, Hector dies, the Trojans lose) was well established, I can see how someone well skilled in the bardic tradition could flesh out the legend and compose a good tale all by himself. That said, there are some indications that the stories as we know them now might have been somewhat edited at the time of Peisistrotos. Homer almost certainly existed and he was undoubtedly an Asiastic Greek with pro Ionian or Aeolian prejudices/viewpoints.
The intro to my copies of the Iliad and the Odyssey both say that the issues of whether there was a single person and whether that person was named Homer who wrote the Iliad and the Odyssey is not resolved.
I remember from my literature classes at Uni that there was a great deal of dispute about the issue. From memory, no resolution has ever been reached. Keep in mind that these were oral stories that were passed down over centuries and would have changed considerably over time.
I believe this issue has been discussed in this forum before, so you might want to do a search.