1) To answer that fully we will need to dig into what is a factual statement. I would gladly discuss the nature of facts but don't find this to to be the forum.
But my basic believe is that facts are true in context. Relative not objective. Facts (reductional interpretations of reality) are described from the vantage point of the observer. We can experience what we call reality in a certain way but not in all possible ways.
And that is all fine and good. We don't need true, just useful.
2) We evaluate them within the different clusters we live in. There are people who believe that holocaust never happened. There are people who believe that 9/11 was orchestrated by the US. Most people though believe the same things. World War I broke out in the year 1914.
That does not by any metrics mean that that is a true statement. You could very well argue that it broke out way before that. Cause I take it you agree that people didn't wake up one day in the year 1914 and thought, let's have a war.
The coherent sets of beliefs used to be mainly cultural now they'r exposed on the internet. And people form around various perspectives. So you have clusters of perspectives. That is why you have what seem to be agreement on those perspectives.
That is why there aren't anyone claiming that the Alpha Centaurions secretly invaded the planet to initiate I or II WW. It could be true but there is nothing factual (and again I refer you to 1) ) to construct that belief.
There are however many other conflicting and competing view. Less about the factual parts (D-Day) more about the meaning of that day. The factual parts are not really that interesting and they are certainly not important. Only to the people who actually where around at that time.
As long as you know that it happened 6 June 1944 +- a couple of days or months (with time and as the people who lived at that time dies, the accepted +- span will grow ever bigger) you are ok.
3) Again you are confusing two things here. There are factual statements (that might or might not be true and again I refer you to 1) and then there is the interpretation of these facts. I am more concerned with the latter part than the first.
4) There is nothing big in that claim. I would be happy to discuss this further but not here. Kuhn, Lakatos, Feyrabend have all done a fairly good job at describing some of the problems with believing in objective truths. I have my own views. We can discuss but then we should find a place to take it. Hmm maybe there is even a small side project idea there.