Most of the New Testament writers were contemporary in that time. The manuscripts universally accepted for the 'canonized' collection known as the New Testament was based on whether the manuscript was written by somebody who was an eye witness to the accounts or who directly knew somebody who was an eye witness to the accounts. Scholars in modern times question that in various cases, but overall, it can be considered mostly reliable.
And I cited those two passages as examples but not necessarily as what I consider the best example which is what you asked for.
No, actually, they weren't. None of the gospel writers were eyewitnesses, neither was Paul. As for the canonization process, it mainly went along with whatever books the version of Christianity that won out and became the dominant orthodox form considered to be non-heretical.
In the first and second centuries there were some wildly different ideas of what Christianity was. For example, the Marcionites believed that the old testament god was an evil god, and a lower god than the true god which Jesus was the son of. Jesus was sent by the real god to save us from Yahweh. They were strongly anti-Jewish as a result (as they thought they were followers of the evil god), and rejected the Old Testament. They also rejected all of the gospels except the Gospel of Marcion which was based on Luke.
The Ebionites on the other hand were a strongly Jewish version of Christianity. They believed in holding to all of the old testament rituals, however they rejected Paul's writings and all of the modern gospels as well. They used the Gospel of the Ebionites instead.
Docetism on the other hand believed that Jesus didn't actually exist physically, and that he was pure spirit. Different groups had different takes on salvation seeing as if he was pure spirit, then he could not die, and therefore was never crucified and died for our sins.
There were groups who believed there was one god, and Jesus was his son. Others thought Jesus was a regular human who was adopted by god. Some groups thought Jesus was god, and some believed Jesus didn't actually physically exist. Some groups thought there were two gods, or ten gods. There was a group that even believed in 365 gods (one for every day of the year). There were quite a number of other wildly different takes on what Jesus was, what his mission was, how many gods there were.
Some of these sects lasted into the 4th, 5th and 6th centuries, or later in some cases.
The only reason the bible is how it is today is because the sect that emerged as the most powerful and dominant one happened to believe in the writings that later came to be canonized as the modern bible. At no point in the early history of Christianity were they a majority view, they were just one of many sects, and they eventually got the most converts and amassed the most power. When they got powerful enough, they actively snuffed out all other sects they thought were heretical.
That's it, there's no basis in fact that went into it. If the Marcionites had won, we'd have a totally different holy book, with just as much evidence backing it. In fact, I think the Marcionite take on things actually makes more sense given the state of the world. Their version of Christianity at least fully addresses things like the problem of evil.
Lastly, and it should go without saying, if there were all of these wildly different sects right at the beginning of Christianity, then how much basis in actual fact could there have been? If there was a Jesus who walked the earth and gave a clear message on what he wanted done, it's almost unthinkable nobody agreed on the core fundamentals of the religion mere decades after he was said to have lived.
