Those are all decent overviews. Can you say what specifically you're interested in learning more about? I might be able to help on the middle period (9th-12th century) if so.

Children were either home-schooled or went to private schools. Literacy was high, esp. considering the European average at the time. In the early period, emperors founded universities, or at least, centers of higher education. In later periods, these state-founded institutions usually didn't last more than a generation and were replaced by private schools of higher education, of which there were many.