Citing apologetics websites from people with no relevant education on the Biblical texts is really not meaningful. Like you, the website largely cites the Bible on the assumption that its claims are true. This is entirely the habit I am questioning.
Regarding whether the Gospels claim to be eyewitness accounts, you (and the website) are simply incorrect. The Luke 1 passage, for example, does not say that the author was an eyewitness. It claims that the stories were "handed down" from eyewitnesses - meaning Luke is a second-hand account at best. None of the non-Gospel passages mention the Gospels, so they are irrelevant.
Again, these Christian apologetics websites you are citing are simply inaccurate. I would highly encourage you start reading some of the peer-reviewed academic literature out there on the nature, composition, and accuracy of the Gospels. Mark, the first Gospel to be written, does not "clearly teach" that Jesus appeared to many people at all. It ends with the women finding the empty tomb, being afraid, and telling no one about it. (Mark 16:8 - before you cite any verses beyond that, it's well established that the verses beyond 8 are not original to the text and were added later.)
Your claims, and the claims of the website, again stem from just citing the Bible's claims as fact. The largest reason Christianity had such a huge rise in adherents within 300-400 years was its establishment as Rome's state religion, culminating in the outlawing of paganism in the late 4th century.
I don't see this conversation going much further if you are simply going to continue quoting the Bible as fact, when that is exactly where we disagree. I'll give it one more round if you want.
