If you have a decent bible, maybe a full copy of the NIV, read the introduction to the gospels. It will tell you that there is no confirmation on who wrote these gospels. The copyright page will also show you that there is no accredited authors to the whole book.
That's the only truth in the bible I know of.
As far as Jesus (if he existed) being literate, chances of that are almost zero. Although he may have quoted from the Talmud, over 98 percent of the local population were in fact illiterate. It would cause quite an emotion among people when the poor son of a carpenter born in a stable could actually read. Reading was for the wealthy. There is no evidence or any passages mentioned that Joseph or Mary could read either.
According to Luke, Jesus could read.
After reading from the book
of the prophet Esaias Jesus closed the book.
Luk 4:20 " And he closed the book, and he gave [it] again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him."