To say this is to say that there are additional written primary sources or archaeological evidences that attest to Jesus's resurrection. I'm not aware of such things. I'm only aware of the books of the New Testament. All later writings I'm aware of aren't primary sources.
I would refer you to James Warner Wallace the author of the coldcasechristianity web site.
He as an atheist and working coldcase detective was challenged to use his detective skills on the new testament.
The results of his investigation was that he was convinced of the accuracy and reliability of the gospels and he became a Christian.
Or there is Lee Strobel and the case for Christ.
As an atheist investigative reporter he investigated Christianity to prove it false. He could not and again convinced by the evidence he became a Christian.
Read there stories and there investigations and present your evidence that shows they are wrong.
I don't know. If the answer was "never", then that would be a point against the believability of the gospel accounts. If that answer was "rarely/occasionally", then we would need more evidence about the effects and circumstances of Jesus's resurrection to properly evaluate whether it was the most important resurrection ever.
I don't think that's necessarily the case. Those details might be accurate, but other details may not be. There's no reason to believe that a single gospel account is the recollection of a single eyewitness. They could be compilations of stories and ideas from multiple people.
They were convinced of something. We don't know how many were and were not.
Furthermore, we don't know that they did ultimately. There's a lot of stories about the martyrdoms of the apostles, but there's is no way to confirm those claims. I have no idea if Peter stayed faithful but Thomas didn't. I have no better evidence for this than whether Thomas visited India, China, and Indonesia, claims found the same generation of 2nd and 3rd century texts.