1. How come no one witnessed all these Christians being raptured? I think the best answer is that it happened truly as Jesus forewarned, like a thief in the night. The same time that that the priests were ministering in the Temple and heard the voice saying “Let us depart from here”.
In an earlier post I had gone into more detail on this, including the quote from Josephus on this event. IMO, I think the “depart from here” was a reference to those just then leaving Hades, followed a split second (or less!) by those on Earth.
The fact that this was at night and that many Christians were being hauled away, never to be seen again, just like Paul had been doing three decades earlier, help to make this more under the radar.
2. Why did no one write about this supposed removal of all Christians from the Earth? And why did those contemporary Christians like Clement and the writer of the Didache not mention it? I would reply first of all that there was not a lot of writing going on then. Or the writings were not found. Many of the writings supposedly from the subsequent two or three decades are better dated prior to AD70.
The Didache and Clements letter to the Romans come to mind here. Both of them refer to Temple rites still ongoing. Both are often erroneously dated after AD70. For that matter Johns Revelation is also erroneously dated. He thus, consequently, made no mention of the destruction of the Temple, but rather described it and the rites as still existing.
3. What about the persecutions still happening after AD70 at Pella and elsewhere? I would say that if there are no longer Christians on the Earth what happens then it is not persecution but payback. The ones still left behind are those who remained unconvinced by the Gospel. However outwardly righteous they may have been they were strangers to the righteousness of God.
The detailed account of Josephus of what happened to the Jews in Pella, Masada, Antioch, and other cities throughout the Empire show God’ s retribution on those who obstinately refused His midnight call for repentance.
4. If the Christians were all raptured from the Earth how did Christianity start again? Although the Christians were gone, their writings were not. And if God, as Jesus said, could make “sons of Abraham” from stones surely He could – and I believe He did – grow new saints out of the writings left behind by the raptured older saints.