I am assuming the audiologist determined your boy hears perfectly well. So, as for the singing, I think that may have more to do with his vocal cords and throat arrangement, especially since he had problems eating as an infant. I mean, forget the words, and see can he hum all over the scale. But that, too, requires the vocal cords to cooperate, so that might not be the problem, rather a throat thing. But I think if an ear nose throat ENT doc checked him over (diff from an audio guy), could be he'll at least determine if the problem comes from his vocal cords and/or throat somehow. Another possibility is, since you mentioned he has trouble reading, he might need to have his eyes checked, to make sure he's seeing well.
You also talked about memorizing, and could be the part of his brain that retains music and the written word is miswired somehow, and also maybe he has a neuromuscular problem having to do with speech, altho I don't know too much about that sort of thing. But someone who works with kids who cannot read well may be familiar with the sorts of health issues that might cause that to happen, and they can direct you to the proper specialist for that, including a speech therapist or a neurologist, which he might order an MRI to have a look at what's going on in the brain. So, those would be my ideas.