Okay. This is fun. I have been slow to post on this thread because I read these posts and the words make great sense but the concepts leave me with nothing, which means I re-read until it starts making sense. Thankfully,
choirfiend and
mike have posted such helpful replies!
What I have gathered:
parish ---> diocese ---> Synod/council
These Synods are designated "autocephalous." They are led by a leadership of equally ranked Bishops, with a Metropolitan selected as a "chairman."
Due to historical events including the Revolution and the era of Immigration, the Orthodox parishes and dioceses in the USA are under the jurisdiction of various Synods. These Synods, in America, are sometimes "national" because of the need to appoint a bishop and circumstances dictated they selected from what was available?
Yes. If you had 1,000 immigrants from Greece in NYC, they established parishes made out of greeks. After the Russians were in trouble, the parishes returned to the authority they came from, and they are governed by their bishop, who now reports to the Ecumenical Patriarch, who is back home in Constantinople.
Kinda like how the states were settled---Americans moved there, established some government, and became part of the US government. Greeks moved here, established parishes, and b/c the Russians weren't in a position to be governing them, returned to the government of the homeland. The same can be said for any ethnic group.
More questions:
Who grants/granted the designation of "autocephalous" to the various Synods in the first place? Was it consensus? By whom?
Consensus by the council of bishops in the homeland that those parishes came from. For example, the Orthodox Church in America (OCA) is the jurisdiction that remained in the US of the Russian mission parishes. They remained under the rule of the Russian Orthodox Church until 1970, when the Russian Orthodox Church granted "self-rule" or autocephaly to the OCA.
If the Greek Orthododox located in America were to become autocephalous, the decision would come from their governing bishops--The Ecumenical Patriach and the bishops in his jurisdiction. Make sense?
Regarding the "national" titles, how much of the national/cultural aspect is present in the individual parishes/Synods? I mean, even if the theology is the same, are there cultural differences? And if so, well, my woeful Greek is Attic, my Arabic is just passable, and my Russian is non-existent. Not to mention all the other relevant cultural factors - family history, food, etc. How much of a role does this play? Choirfiend mentioned that there would be such differences, but how much do they matter?
That depends on how much any of those given cultural elements bother you. Most parishes serve the services in English or a mixture of English and the "homeland" language. That can make sense if half of your congregation speaks Russian--then you gotta do some in Russian! Very few parishes are completely in another language. If they are, their congregation is likely to be brand new immigrants who don't really speak English, or at least, should be ministered unto in a language they grasp well. Nearly all OCA and Antiochian parishes are completely in English. Most Greek parishes will have a mixture of Greek and English.
The musical styles will be different. The architecture may have a different "flair." Russians have those onion domes that they are known for.
And yes, there is a difference in the food at coffee hour. I've been trying to get to a Greek church for some Greek food at a yearly parish festival for 2 years!!

mmmmm spanikopita!
But those differences are superficial. Kind of like being Italian Catholic, Irish Catholic, or Polish Catholic. You may eat spaghetti, corned beef, or cabbage rolls, but you're still Catholic. You can be Greek, English, or Russian, but you're still Orthodox.
Additionally, many parishes have many people who have become Orthodox and bring wtih them whatever their cultural traditions are--regular ol' Americans too. Each parish has a different cultural feel b/c of the makeup of its parishioners! There is only one Orthodox Church in my town, and EVERYONE goes there. It has Americans from every background, Russians, Serbians, Romanians, Greeks, Arabs, Ethiopians, Nigerians, and probably others in it.
If doesn't make a qualitative difference, so if it doesn't bother you, it doesn't matter.
It sounds like the Russian Orthodox Church was at the crux of the development of the EO in America. Why do I have this notion in my brain that Orthodox means Greek Orthodox?
Probably b/c that's what you've seen the most of in media or heard the most about. Americans are incredibly ignorant (dont take offense, I'm American too!)
Is there really an Arab Orthodox diocese/Synod? Fascinating!
Sure! I mean, come on, the Church came out of the Middle East!!! If you study Church History, then you know that 2 of the 5 main cities that made up "The Church" are Jerusalem and Antioch. Nearly all the "arab" Orthodox Christians in this country are part of the Antiochian Orthodox Church.
Not to sound daft, but, in other continents, where the Synod is located in its particular "homeland," are there still "other national" Synods too? (Wow, this is convoluted, I can re-write if need be.)
Thank you again for your help (and patience)!!!!
No. Because in those places, the Church spread by conversion instead of by immigrants from 30 different countries all amassing there, there is not this abnormality of bishops from different jurisdictions in the same areas.
Again, here's a link to all the Orthodox Church in its various countries and locations:
OCA - World Orthodox Churches
Did you use that church finder link? What churches are located by you? Often times people here may be familiar with your area and have suggestions to make on finding a nice parish to visit.