Short answers, pulled from the story.
The Nicene Creed is the foundational doctrinal statement of Nicene Christianity, formulated at the First Council of Nicaea in AD 325 and amended at the First Council of Constantinople in AD 381. It defines Jesus as divine and co-eternal with God the Father.
Arianism was the main rival to Nicene Christianity at the time of the First Council of Nicaea in AD 325. Where Nicene Christianity holds that Jesus is co-eternal with God the Father, Arianism treated Jesus as the first among created beings and inferior to God the Father. Arianism was eventually eclipsed during the 7th century AD when the Gothic kingdoms converted to Nicene Christianity.
Nicene Christianity became the officially endorsed state church of the Roman Empire in AD 381, when the Roman emperors formally endorsed it. This status ended following the Council of Chalcedon in AD 451, after which Chalcedonian Christianity became the empire's official state religion.
The Council of Chalcedon in AD 451 was convened to resolve Christological disagreements about the human and divine natures of Christ. It concluded that Christ had two distinct but inseparable natures. Churches that held to a single-nature view of Christ were excommunicated by the Roman Empire and became the Oriental Orthodox Churches.
Non-Nicene Christian denominations today include Jehovah's Witnesses, the Unitarian Church of Transylvania, Oneness Pentecostals, and the majority of the Latter Day Saint movement. The Community of Christ, formerly known as the Reorganized Church of Jesus Christ of Latter Day Saints, is a notable exception within the Latter Day Saint movement and is recognized as a Nicene group.
Yes. The Community of Christ, formerly known as the Reorganized Church of Jesus Christ of Latter Day Saints, is recognized as a Nicene Mormon group. It is an exception within the broader Latter Day Saint movement, the majority of which does not adhere to the Nicene Creed.