They used force
Through most of their history the ancient Romans had their own religion: Roman Religion. In the Later Empire Christianity spread in the Roman Empire, was endorsed by the Roman emperors and became state religion.
Christianity did not easily spread through the Roman Empire. See the related question, "How did Christianity spread throughout the Roman Empire?"
When Christianity was endorsed by the Christian Romans Emperors, these emperors appointed Christian senators.
By 325ad Christianity had spread throughout the Roman Empire and to Britain. If you google "spread of Christianity map" you will find maps showing the spread.
Christianity
Slaughter and suppression of other religions, and it provided a religious hierarchy of bishops which was valuable for emperors to use as a control measure to supplement his secular power.
Christianity differed from Roman state religion in several key ways. The Roman state religion was polytheistic, while Christianity was monotheistic. Christianity also emphasized the importance of personal faith and salvation, while Roman state religion focused on performing rituals to honor the gods and ensure the well-being of the state. Additionally, Christianity challenged the traditional social order by preaching equality and love for all people.
The Romans did not try to stop the spread of Christianity. There were alternations between periods of toleration and periods of persecution. Some Roman emperors thought that Christianity was a threat to the Roman state because many bureaucrats and soldiers converted to Christianity. The Romans saw their state as being interlinked with Roman Religion. The persecutions were aimed mainly at the civil service and the Christian clergy, rather than Christianity as such. The last and worse persecution, the Great Persecution, failed because it was difficult to implement, because of the resistance of the Christians and because it undermined the stability of the empire. After that, the emperors endorsed Christianity, favored it over other religions and promoted it. Eventually, Christianity became the state religion of the empire. With imperial support, the spread of Christianity accelerated.
No. They fed Christians to lions for entertainment!
The spread of Christianity had political ramifications for the Roman Empire. The empire split into two, Constantinople to the east and Rome to the west
No. In fact, for hundreds of years the Roman Emperors did everything humanly possible to surpress Christianity. Until Emperor Constantine, Roman Emperors absolutely hated Christianity. The idea that a Caesar invented the story of Jesus is ludicrous.
It could not decline from nothing - it did not exist until after much of what was to become the Roman empire was already under Roman rule. It spread, particularly after the Romans accepted Christianity under Constantine