Nero was the 1st Roman Emperor to persecute Christians. After him there were many Roman Emperors who murdered Christians. For an example the 3 of the 5 good emperors murdered Christians.
Constantine was the first "Christian" Emperor of the Roman Empire. He made the Edict of Milan which meant it would no longer be a crime to be a Christian. Later however, since he didn't completely under stand true Christianity, he persecuted non-Christians in the name of "Christianity".
The Fall of the Roman Empire was caused by many things. First they were founded on violence which equals moral decay. Next they had no stability in leadership, the Germanic Tribes invaded, and they had poor management of finances.