Regarding the spread of christianity, several factors contributed greatly to it.
1-Regardless of wether one is a christian or not, its pretty hard to deny that the apostles were pretty damn badass and were specifically instructed by Jesus on how to spread his ideals after he went away. The one I mentioned earlier, Paul of Tarsus (originally named Saul) didn't even meet Jesus in person during his whole life, and was actualy a really scary pharisee inquisitor and roman citizen who had special permission from the synagogues in jerusalem to hunt down the "disciples of the nazarene" (IE how the early christians were known). After stoning a very important christian preacher and then being sent to Damascus with specific documents and orders that would allow him to imprison each and every christian he found, due to what he himself described as a miracle, he changed his ways, became a christian and then basically started going around the most important parts of the world preaching about Jesus. He was so damn badass and succesful that he managed to convert many different pagan tribes and form congregations in the most important cities of the Roman empire, while basically travelling on foot most of the time. Other important apostles, such as Peter himself, travelled around and converted many people, among them pharisees, too.
2-A fair bit of caravaneers of the time ended up becoming christian due to having travelled with an apostle and/or doing trade between cities that would later become christian (such as Antioch, a very important city at the time).
3-Like mentioned above, the people of some key centers of trade in the Roman Empire ended up converting to the new christian faith. Even after being systematically persecuted by local synagogues, the heads of the temple in Jerusalem and the Roman Empire, they persevered, which eventualy culminated in the conversion Emprah Constantinus, which may have converted because, at a certain point, he started viewing the citizens of the empire as mostly christians.