You have several questions here. These are short and dirty answers, and can be clarified if you are still interested.
1. The originals, i.e., the autographs, do not exist, or, if they do, are unknown. That's pretty common in ancient situations. They would have been copied and passed around pretty extensively, all in the first century. There was already a long-established and exceedingly meticulous mechanism in place to copy manuscripts with a high degree of accuracy.
2. There are hints of documents written shortly after the fact, but in many cases, it would have been highly unusual to have had the kind if instant biographies we now enjoy. There was no real point in writing about someone you could simply go and talk to. It is only after a person dies that the memories are recorded, assuming the person was a figure of great significance. Recall that the life of Socrates, such as we have it, is rendered after the fact. Even the caesars had little or no such luck.
Memories were a lot longer and more accurate, by virtue of necessity, training, and practice, so drafting a memory even decades later would have been no problem. Recall the lyrics to 'Twinkle, twinkle, little star." You probably haven't thought of them for a while, but they can be recalled perfectly. We are sloppy today because we have so much written down, and so can afford to be sloppy. Back then you needed to be able to remember things on a single hearing in order to survive, literally. Whole conversations could be (and were) remembered verbatim over the course of days during typical philosophical conversations, and could easily be remembered for years and decades.
While there are no known writings from during the life of Jesus (nor should we expect there to be, for the above reasons), we do have interesting odds and ends from an antagonistic point of view, such as Roman graffiti from the first century mocking the crucifixion of Jesus.
Some of the gnostic works, such as the gospel of Thomas, purport to record events in Jesus' life, but those were written much, much later, in some cases a couple of hundred years later, and their style and tone is so absurd and anachronistic as to render them unbelievable even if their dates could not be verified.
Again, that's the short version. Hope it helps.