Although almost nothing is known about the author of "The Iliad" and "The Odyssey", they are commonly attributed to a blind poet named Homer. We know only that this person lived a long time ago, between the Bronze Age and Iron age, and that he or she spoke ancient Greek.
I have never heard anyone doubt the validity of who wrote these epics before. I don't think there's anything to really dispute who wrote the books. But it's also such a long, long time ago that we can never really get confirmation on who truly authored those stories. So it's a toss up.
At a point, this is a meaningless argument because it can never truly be proved that he did or didn't write it. I believe that he did, simply because it was attributed to him for so long. Now I'm not sure if he had any help or if it was just an oral story passed down and he wrote it. But I think that it is Homer's masterpiece.
No, I don't believe that Homer was the author of the Iliad and the Odyssey. These great literary texts were written far too long ago to accurately know who the authors of them were, and though the Greeks were known for their historical accuracy passed on through the generations, there is no real and absolute way to judge who the actual authors of the Iliad and the Odyssey were, similar to how we cannot with any conviction say who the authors of the Old Testament were.
I think that "Homer" is just a person who they attribute these stories to, and in reality we have no idea who really wrote them. They could have been oral stories passed down, and finally put in words (much like the bible) by a series of writers. It is impossible to know.