First: Welcome, Andrew! You sure picked a loaded set of questions. As SolEX01 has pointed out, you can get a bit of information from our previous discussions here by utilizing the Search function. However, I'll try and provide some answers as best as I can. I'm a bit time limited, but here are my first thoughts:
- Why are the Orthodox set up in Nationalistic Churches? What happened to the ancient original model of only 4 Patriarchates in the Communion?
The movement towards "Nationalistic Churches" isn't neccessarily 100% innovation, considering that Cyprus was "independent" (or whatever we want to say - autocephalous is the prevailing term, although it seems to be a bit loaded) since the beginning, and since the kingdoms (predecessors of "nations") of Serbia and Bulgaria had enjoyed some sort of independence before the final sacking of Constantinople. There were 4 Ancient Patriarchates (and then 5) in one empire,
so we didn't have an opportunity for "National Churches." The situation of "National Churches" arose when (a) Nations were formed, and (b) when the 4 Orthodox Patriarchs (who were at one point all under Moslem Rule) had diocese that were in "free" (non-Moslem) territory.
However, the current system is only partially "nationalistic." While some of the Churches are restricted to their own national border (Greece, Cyprus, Serbia, Bulgaria, Romania), others are not (The 4 Ancient Patriarchates and Russia), and most have "diaspora" parishes and diocese in Asia and the "New World" (N & S America).
- How can the Orthodox claim to have unbroken succession in regards to the Patriarchates of Antioch and Alexandria? The original holders to them are the Syriac and Coptic Orthodox Churches, respectively.
Well, I suppose it is a matter of perspective; we believe that the "original holders" of the succession are still in the Orthodox Church, and those of the Syriac and Coptic Orthodox Churches are bishops who came from schism.
- How far away is reunion between the Oriental Orthodox and Byzantine Orthodox?
I don't know - it depends on whom you ask. My Metropolitan (MAXIMOS of Pittsburgh) thinks it could be very close (in fact, iirc, he thinks it is a shame it hasn't happened yet, as he feels we are very capable of healing that rift); others see it as a distant, but possible, reality.
- Why do the Orthodox allow for overlapping jurisdictions? I had thought that the original model was only one Bishop for a certain area.
Well, it's really just a concession at the moment - no one really likes it. One bishop per area is pretty much the prevailing model, although the idea of ethnic parishes isn't actually a new thing (Fr. John Behr points out that in the 2nd century there were ethnic parishes in Rome, iirc).
- What is the definitive role for the Patriarch of Constantinople? Is he a "primus inter pares" figure or does he do more than that?
First Among Equals is about it. There is a few additional roles granted the Synod of Constantinople (seat of final appeal, etc.).
- Why are some jurisdictions allowed to not recognize another? For example, Estonia is in communion with Constantinople and Russia is in Communion with Constantinople, but Russia and Estonia are not in communion.
Actually, Estonia is in Communion with Constantinople, Constantinople with Russia, Russia with Estonia - but Estonia not with Estonia (there are two hierarchical structures there right now, one in communion with the EP, one with the MP).
Why? Because the Church, while being One Body of Christ, still maintains its local ("incarnational") character - local churches bound together by faith and Communion. So it is, and always has been, up to the local Churches to maintain, define, and promote Communion, Doctrine, Synodality, etc.