Around the time of the 1st council of Nicaea (325), what was the makeup of Bishops at the time?
This was a first ecumenical church council, on which the bishops gathered together to settle the raging of the heresy of Arianism. It is recognized by Eastern Orthodox, and Roman Catholic churches as real ecumenical council. It was the first ecumenical council, although there are many other local councils, beginning with the first Apostolic council, were gathered to solve a various range of problem that stand before the Church of Christ in those times.
I read that 1800 people attending this council, but was this a fair cross-section of followers of Jesus or was it influenced in one direction or another?
That was the real Jesus followers, i.e. people of His church, that have a valid rights to make a counsil in name of Christ. The main formulae of the councils was like the following:
It deigns to Holy Ghost, and to us.
That means that the council solution (of course verifyed by time) is not only from men, and from God too.
I heard that at around 360, the dominant understanding of Jesus was more of an adoptionist belief, is this true historically?
If you mean the time between the two ecumenical counsils, the most of church's creations like Divine Liturgy, monastic orders, etc were developed or finally adopted in that time. However there are people that have the adoptionist belief of course, but such people was in all times including Apostolic.
After people were exiled and executed and books burned, when was the creed established as the dominant creed and pretty much no-one else believed otherwise?
Although the state can execute and exile the people, I think there are really a little bit of them were executed at those time, even Arius has dead with his own death. The state really executed only those people, which it treats as dangerous for it, but the since the Church was under the state, anyway it tried to save many lives even heretics. Therefore I don't think that all of people lost their faith.