The key phrase being “in a literal sense”, I suppose? You believe he considered himself to be the son of God in a sense different from a less-literal sense in which “we are all children of the Most High” (Psalms 82, IIRC)? Umm, cite?
Psalms 82 is how he defended his right to refer to himself as such when accused of trying to make himself a God.
Feel free to develop the assertion that he really meant, as Chevy Chase would have put it, that he’s the son of God and you’re not. But I don’t accept as a “given” that he meant anything of the sort.
Probably not. Remember that this is Herod, of whom Augustus said “It’s safer to be Herod’s swine than his sons.” I’m not at all sure the death of a few dozen peasant babies would have seemed unusual enough to record…
Another aspect of the question would be, that people often tend to overestimate - vastly - the amount of information we have about the Roman era. For some things, yes, we have lots. But to the best of my knowledge, there is only one literary reference to the destruction of Pompeii. That’s a whole town, including fancy villas, gone in one of the more lurid disasters of history.
The census presents other problems, because there by accident we actually have a little evidence. An inscription mentions Quirinius, and helps suggest his dates.
But in general, I think it’s helpful to bear in mind that we’re missing rather a lot of evidence for the era. Much of what survived, survived by accident. And lots of things which (from a later perspective) we would have been interested in, nobody ever wrote down at all.