The questions and objections covered in these videos are :

Can we trust the New Testament as a historical document?
Hasn't the Bible been rewritten so many times that it can't be trusted?
Wasn't the New Testament written hundreds of years after Christ?
Was the Bible changed?

Can we trust the New Testament as a historical Document?

Scientifically speaking, if you cannot trust the Bible as a historical document then you cannot trust any ancient document. Because there are more copies and fragments of the New Testament than there are for any ancient document in the world.

Hasn't the Bible been rewritten so many times that it can't be trusted?

People make this claim because they're not aware of how the Bible was translated. Author Matt Slick from CARM.org said the following of this objection :

"This is a common misconception. Some people think that the Bible was written in one language, translated to another language, then translated into yet another and so on until it was finally translated into the English. The complaint is that since it was rewritten so many times in different languages throughout history, it must have become corrupted . The "telephone" analogy is often used as an illustration. It goes like this. One person tells another person a sentence who then tells another person, who tells yet another, and so on and so on until the last person hears a sentence that has little or nothing to do with the original one. The only problem with this analogy is that it doesn't fit the Bible at all." [1]

Wasn't the New Testament written hundreds of years after Christ?

This is actually a really important question that plays into the trustworthiness of the message in the New Testament. What most fail to understand is that the crucial gap is not the gap between the time of the evidence and today, the crucial gap is the gap between the evidence and the events described by that evidence. If the gap between the events and the evidence for those events is short, then how long it has been since the evidence and those events to the present day is just irrelevant. Good evidence doesn't become bad evidence simply because of the lapse of time.

And with regard to the New Testament when we look at the evidence, what we discover is that these records of the life of Jesus were written down within the first generation after those events, while the eyewitnesses were still alive, with people who had first hand contact with those who had accompanied Jesus within his lifetime. So that we actually have better sources for the life of Jesus of Nazareth than we do for most of the major figures of antiquity.

Was the Bible changed?

This is a claim that is made all of the time. Now again going back to our 5,600 copies of the Bible that are 99.5% in agreement with one another, they are also from vastly different time periods and were discovered in many different countries. If anyone had attempted to change any of them, it would be the most obvious thing to everybody.

All you would have to do to prove that the Bible had been changed is to find one copy that said one thing at an earlier time period and then find ones from a later time period that said a different thing. It would be the easiest thing ever to do. It would be impossible for a forger to change all of those 5,600 text without being noticed, most of which had not even been discovered yet. This is why people only make the claim that the Bible was changed and why you never find anyone offering proof that it was changed.