Answer

Hello Sh.,
These are long questions, and I’ll try to address them briefly.
I’ll preface by saying that I sent you a link to my notebooks, and there I try to show the chain of reasoning that begins with proofs for the existence of God (the first four), and on that basis proceeds (in the fifth) to the revelation at Mount Sinai and obligation to the Torah. I explain there why it is not correct to deal with each such stage separately. I suggest that you read it there.
 
 
I don’t really understand what is meant by an act of sorcery by Moses. Do you know sorcerers who can do such a thing? So why assume that at all? Why is that more reasonable than accepting that if someone revealed Himself there and said He is God, then apparently that is what happened there? Why assume some sort of mass fraud? What would be the interest in doing that? Conspiracies need some sort of indication in order to arouse suspicion. The fact that there is some other hypothetical possibility is true of almost any fact you might present to me, and still I do not become suspicious unless I have good reason for it.
 
1. I wasn’t there either. I also wasn’t at the particle accelerator in Switzerland when they discovered the Higgs boson, or at the Battle of Cannae of Hannibal against Scipio Africanus, and still I accept what those who were there report, until proven otherwise.
2. One could just as well ask how people sin even though they believe in something, down to our own day. How do people eat fattening foods even though they want to diet? How do people steal? Human beings are complex creatures, especially in times of distress, and such actions stem either from some interest or from some impulse. The Sages themselves say that in the past there was an impulse toward idolatry like the sexual impulse that we know today, and over the years it was “nullified” (in my view meaning: it dulled and underwent sublimation). Just as today people can sleep with another man’s wife even though they themselves know it is wrong, because they have a strong impulse. In the past the impulse toward idolatry was strong. Today we do not recognize that impulse (because it has dulled), and so it is hard for us to understand. But take an example from the impulses that remain (such as sexual prohibitions).
I do not think there are many examples, if any, in history of an entire people believing in a chain of events that they are told they all experienced themselves. The examples usually brought for such “revelations” are never really similar to our case. There is a discussion on my site with references, and you can see it there.
https://mikyab.net/%D7%A9%D7%95%D7%AA/%D7%94%D7%94%D7%91%D7%93%D7%9C-%D7%91%D7%99%D7%9F-%D7%9E%D7%A2%D7%9E%D7%93-%D7%94%D7%A8-%D7%A1%D7%99%D7%A0%D7%99-%D7%9C%D7%A1%D7%99%D7%A4%D7%95%D7%A8%D7%99-%D7%94%D7%AA%D7%92%D7%9C%D7%95%D7%99%D7%95/
There is another thread on my site that deals with this and gives sources, and at the moment I can’t find it. You can contact Maor Ovadia, whose email I sent you, because he worked on this topic.
 
As for your last question about statistics: this is an argument that has come up recently (mainly in Nassim Taleb’s book The Black Swan about the stock market), and I mentioned it a bit in my post about the law of small numbers.
I’ll give you an example that makes it clearer than a theoretical discussion. Suppose you rolled a die many times and got 6 a thousand times in a row. Would you attribute that to chance? After all, it could be chance. If someone won the lottery 50 times in a row, you understand that police would come arrest him, even though it could happen. Why? Because although it could happen, the probability is tiny. It is more reasonable that it was intentional.
Now think about another case. In rolling the die you got some arbitrary sequence of numbers. That of course proves nothing, because some sequence of outcomes had to occur. But if someone had told you in advance that this is exactly what would happen, of course you would be very surprised and would look for an explanation, right? (Even though it could still be random.) If the Torah says in advance that the Jewish people will go into exile and survive and return to their land, etc. etc., and that the eternity of Israel will not prove false, despite persecution and harassment, then it is hard to attribute that to chance, because it was said beforehand.
And again, I return to my first remark here. There are two hypotheses to explain the uniqueness in our history: 1. Chance. 2. Intention. Indeed both exist, but think which of them is more plausible. There is never certainty, but we must choose our position based on considerations of probability.   
 
I again return and suggest that you read the fifth notebook.
 
Happy holiday