Short answers, pulled from the story.
Christian theology begins with the Bible, a collection of texts that Christians believe were written under divine inspiration. The Old Testament and New Testament form the primary source material for theological study.
By the end of the 4th century the Trinitarian doctrine was widely held in its present form. This development followed centuries of debate among early church leaders including the First Council of Nicaea convoked by Emperor Constantine in the 4th century.
Arianism taught that Jesus was divine yet created by the Father making him less than God himself. This belief system where Jesus's divinity differed from the Father's heteroousia remained popular in northern and western provinces well into the 6th century even though it was condemned at Nicaea.
Pneuma means breath in Greek describing a non-material being or influence. Within Trinitarian belief the Holy Spirit is equal with God the Father and God the Son yet proceeds from them as described in the Nicene Creed.