We don't really know who Paul is just from the fact that he's telling his story. He could be anyone - a regular person, a professional in some field, or someone with a unique background.
There are several things. First, we might get to know about his personal history, like where he grew up and what his family was like. Second, his story could reveal his dreams and how he pursued them. Third, it can tell us about the people he has met and how they influenced him. If he shares a story about a difficult time, we can see how he coped and what strategies he used to get through it. In short, Paul's story has the potential to be a rich source of knowledge and inspiration.
Again, without more details, it's hard to say. But if he's sharing his story, he might be a person who values self - expression and wants to connect with others on a deeper level.
It could be to the reader. Often, narrators in novels or short stories are implicitly addressing the reader, sharing their tale as if we are the confidants.
Odysseus is telling his story to the Phaeacians. They are a kind and hospitable people who offer him shelter and listen to his long and arduous journey.
One purpose was to expose the horrors of slavery. By sharing his own experiences, Equiano aimed to make the world aware of the inhumane treatment slaves endured, such as the brutal conditions on slave ships and the dehumanization they faced daily.
Odysseus shares his adventures with a group of people in the court of the Phaeacians. King Alcinous and the other members of the court are the main recipients of his tales.