I would say that 1st Nicea was primarily about the Incarnation (well okay, they also decided a bunch of other stuff, such as whether it was okay to cut one's manhood off on purpose), and only secondarily involved the Trinity. The problem is easy to see: If Christ is the son of God, does that mean God created him? The correct answer, apparently, is no--he is rather "eternally begotten of the Father."
While this does impact upon the doctrine of the Trinity, 1st Nicea was rather uninterested in the Holy Spirit, and the existence of the Trinity seems to have been widely assumed. The doctrine goes back to the second or at least third century AD (unless one insists on the Johannine comma), and makes sense if you consider that all three elements of it were objects of worship--in a religion which claimed to be monotheistic. The point of Nicea was to establish what this means exactly. (You can still confuse people by asking them whether Christ is the Son of God, or God himself!)
The "rules of order" were real vague, and it is apparently Orthodox doctrine that a council is invalid if the people rise up and oppose it--for example, by rioting in Byzantium.
The so-called Nestorian (split off after the second ecumenical council, opposing the third) and non-Chalcedonian churches (this is the fourth council) are still around, and it is the last group which is historically (but no longer) identified with monophysite belief. They include the Coptic, Armenian, Ethiopian (and Eritrean!), Syriac, and in India, the Malankara Orthodox Syrian Church / Church of the East.
Prester John is indeed a myth--he was supposed to represent a faraway Christian kingdom that offered Europe hope against the Mongols--but might have been based on dim historical memories of Nestorianism. The group in India you're thinking of is probably the St. Thomas Christians of Malabar, who are divided into the Oriental Orthodox group mentioned above, a Uniate group (in communion with the Roman Catholic Church), and a Protestant group which belongs to the Anglican Communion. They claim that St. Thomas voyaged to India and founded their church, and they do seem to be almost that old. Various external powers persuaded some of them to make alliances, resulting in all these contradictory identities.