I would love to learn more about the differences between these churches, what caused them to split, what relationships they had with each other after and what differences are still true. I'd also like to have a follow up of the difference between Russian Orthodox and Greek Orthodox, and if they are connected historically.
Off the top of my head I can't answer all your questions but something you might find interesting is that these churches were reconciled during one of the crusades when a European prince became the ruler of Constantinople.
Also one of the goals of Pope Urban II in launching the First Crusade was to reconcile the Orthodox with the Catholic Church. Emperor Alexius Comenus had asked the pope to send Knights to the Levante to save his kingdom from the Seljuk Turks. Urban hopes that sending him aid (and launching the crusade) could reunify the two churches.