Yes. Eastern Orthodox, which split off from Catholicism during the Schism, arose from the same gradual development of doctrine and practice that continued well into the Medieval period.
2) Read the Early Church Fathers... in their writings, you see clear bits of nascent Catholicism/Orthodoxy. You do not see nascent Protestantism.
You know what's funny? I DO read the patristics. I have the complete set on my home computer. Reading them has done more than anything else to convince me of the AHISTORICAL nature of Catholicism, that whatever else they may have been, they WEREN'T Catholics, no matter how much Catholicism tries to claim them.
I have a lot to do today, and I don't really intend at the present time to get into a whizzing match with some Catholic apologist on a facelsss internet forum about whether Irenaeus believed in the "Real Presence" (which he didn't). Will check in later, perhaps.
Having also read some Patristics, I find that claim EXTREMELY difficult to believe. The doctrines are there, albeit often in an incomplete form, but they're there. Certainly, the anti-Sacramental, Sola Scriptura approach is not.
Also, you have failed to answer what we make of the first 1024 years before the schism. Where did they go wrong to make what became the Catholics and Orthodox?
For what it's worth, I don't expect an answer.