When Nero came into power, persecution of Christians skyrocketed. They were tortured, murdered, and put through intense amounts of pain. This lasted for hundreds of years, through many emperors who all acted terribly including Nero, Septimus Severus, Trajan, and more. But in the end, more people became Christians.
Constantine was the first person to legalize Christianity, because he was a Christian as well. However, his vision of Christianity was messed up, and he began to persecute anyone who was not a Christian. He also established the capital of the Eastern Roman Empire, which he named Constantinople.
Many things added up over time to result it the fall of the Roman empire. The force and violence it was found on, and the instability of leadership lead to weakness. And soon Germanic tribes invaded as the army was not as large or strong as it had been before.