A lot and a little.

During the reformation there was correspondence between Protestant theologians and the Orthodox churches. For example, in 1559 Philip Melancthon wrote a circular letter indicating that he hd sent a Greek translation fo the Confession of Augsburg to the Patriach of the Byzantine church. This letter is carried by Demetrios who has spent time in Wittenberg having been dispatched by the Patriarch in order to get information on the Reformation. Melanchthon received no reply, but the Tübingen theologians ade contact with the patriarch Jeremias II. Again the Patriarch is sent the Greek translation of the Augsburg confession. This is 1574, and he respondes with a commmittee of Orthodox theologians to look at it and write a response. It is not highly critical of Lutheran doctrine, but it maintains an Orthodox line. In 1577 the Lutehrans send a reply, highlighting 3 particular points of difference, particularly regarding Free Will, the place of Works, and the relationship between Scripture and Tradition. A second reply from the Patriarch comes in 1579 upholding the Orthodox position especially regarding church tradition and against the Reformation reliance on Scripture alone.

In the early 17th century a certain Cyril Lucaris became Patriarch of Alexandria. He had been involved with Jeremias II and so had some knowledge already of the interactions with the Lutherans. Then from 1620 he was elected as Ecumenical Patriarch, a position he held five times (being also deposed five times). Cyril Lucaris appeared sympathetic to Protestant doctrines, especially when Protestants published a "Lucarian Confession" in 1629 in Latin, in which the Patriarch appeared to endorse Calvinism, and from 1629 to 1633 an "Eastern Confession of Christian Faith" was also published under his name in latin, Greek, French, German, and English. Again, it is unclear whether Lucaris actualy held these views, but he did not disavow them in the written evidence. Cyril also maintained correspondence with the Anglican church, and sent students to study in England, Switzerland and the Netherlands.

However these initial contacts didn't really amount to anything. It became clear to both sides that there were fundamental divisions not just in theology, but theological presuppositions, and politically and culturally the Orthodox church was quite distant from Protestantism, even though in some particulars it was closer to Protestantism than Roman Catholicism. For these reasons the Reformation did not really impact the Eastern Church that much.

Jan Rokyta was a protestant theologist who gave a speech at the court of Ivan the Terrible explaining his faith; Ivan later sent him a letter denouncing it. Peter the Great introduced divorce and forbade to marry people off against their will (or to send them into a monastery) under the influence of what he had seen in Northern Europe.

Should have added this in the main question, but I also meant to ask the same for Ottoman-occupied Christian territories.