My grandma and mom always told me that Mohammed was an analphabet. But maybe he could read and write a bid. I heard that he thought he knows the Torah better than the Jewish people and claimed to be a prophet. The Jewish people did not agree with him, of course, saw him as a blasphemer. That is why he fell out with them. As you said he did not want to accept the schoolars teaching either. When he is not literate how can he understand them? He changed a lot according to his believe. Maybe that is why every character is suddenly Muslim and Ishmael is the most important son. I guess he did not even know that he was Egyptian and that Egyptian had their very own culture and language which died out. He invented the "Holy War" (it is in the Qoran) and fought against the Jews and tried to force everybody to convert to the Islam. Muslims, who believe in all this, won't want to hear that, of course.
Islam