A) There where two councils of Nicea. The first was held by Constantine, and is probably the beginning of at least the Christian Roman Empire, a diffirent entitity than the Byzantine, which starts with Heraclian.The Christians divided into the catholic and orthodox church around the 6th century (council of Niceia)
The Second, the one you are most likely thinking of, is set in the early 8th century. It is held by the Emperor Zoe (not Empress, oddly enough) and her son Constantine. It is basically a renounce-your-Iconoclasm debate. The two churches effectively split on Christmas Day, 800, with the crowning of Charlemagne as Roman Emperor.
B)The Emperor was the hands of God, the sole ruler that God allowed-the "dominus dominatrium". The Pope of Rome was the spiritual head of the world, the mouth of god. However, the Orthodox church said that because Constantinople was the new Rome, the Patriarch was the "Pope of Rome".
You where a lot more accurate for the early centuries.
This whole is-atheism-a-religion topic is among the stickiest I can imagine, so Ill just say that from a linguistic standpoint I *think* that atheism could be considered a religion in the same way that asexual is considered a sexual orientation.
Communism, however, has much too much in common with a religion to be considered anything but. It has a heaven, a goal to work up to (the state of Communism after the Proletarian dictatorship), a chosen people (the proletarian), an inevitable apocalypse with a day of judgment, clergy (communist demagogues), violent groups (November 17th, the Red Brigades), a rigorous state of mind that must be upheld…..frankly, Sun Yun Moon was right only in including Marx in his list of prophets.