All tales are Anansi's, but especially these. The formal history of this book (probably at least partly fictional) is that Harris heard the Gullah Trickster tales he renders into more conventional English as a child, and wrote the essentially oral tales up in order to introduce them to a wider audience. Ok, he could have done a more sensitive job by modern standards. But at least he tried.
I haven't read this edition. Regrettably, I don't remember which edition I DID read. The edition I read was not illustrated. I would think the illustrations might make a difference, but I don't know if they'd necessarily be an improvement. Reading unillustrated books, one develops one's own ideas of how characters look--and the illustrations too often detract from that. Hard to say, really.
I don't know if it would be worthwhile to write up literary versions of these oral folktales. I've seen such literary versions, and some are pretty good. But you lose a lot by not telling the stories aloud. And dialect stories, though of poor reputation just now, can have their own rhythms and magics, that don't survive translation very well.