The so-called Homeric Question has been one of the most controversial and unsolvable problems of ancient history for centuries. Was there really a Homer, did he really compose the epics, and if so, when did he do so? Apologies for the Wikipedia link, but their page actually provides a pretty detailed overview.

The ancient Greeks certainly believed that Homer was a historical figure. They knew him as a blind poet who lived anything between a few generations to a few hundred years after the Trojan War. Even if he existed, though, he isn't likely to have written the epics, but only compiled them from a range of oral traditions. They continued to exist only as oral tradition for a long time. The first to order the Iliad and Odyssey written down were probably the Peisistratids, tyrants of Athens, in the later 6th century BC. Both in their case and in every known "edition" thereafter, scholars argue endlessly over what they may have ordered to be added or removed.

Traditionally, Homer is said to have lived and composed the poems some time between 850 and 750 BC. Modern scholars, however, rarely accept the historicity of Homer outright; some even prefer to call the creator of the Homeric epics "P", the standard neutral designation for an unidentified author. Many doubt whether the entire epic cycle was composed or written by one person; many hands and interpolations have been identified, and some believe the whole thing was a team effort to begin with, like the works of Confucius or Sun Tzu. The date, too, is uncertain. Using internal evidence (mostly aspects of material culture for which archaeological parallels exist, such as weapons, houses etc), Hans van Wees showed that the Iliad and Odyssey take place in a world that looks remarkably like Greece c.675-650 BC.

Ultimately, the answer to your question is no, we don't really know anything about Homer. We don't know if he existed, we don't know when or where he lived, and we don't know if he wrote the epics - or if he didn't, who did.