Does the Rabbi connect with the distinction Rabbi Uri Sherki made, that God’s revelation through history is what matters, and not who wrote the Torah and when? That is, the Torah is an expression or interpretation of historical events through which we think God is revealed?

I don’t know whether I “connect with it,” but I’ll try to answer whether I agree.
I agree with the claim that the content of the revelation at Mount Sinai is not important, and it is clear that an overwhelming majority of what we do was created afterward. In my view, there are also later additions in the biblical text. I’ve written more than once that authenticity is not a condition for obligation. I am committed to some body of Jewish law regardless of whether it was given at Sinai. As long as it was created through the mechanisms of Jewish law whose foundation we received there.
But he also said that the very existence of the revelation at Mount Sinai is important. Without it, he’d be eating shrimp. I wrote something along these lines in my review of Rabbi Amit Kula’s book, Was It or Was It Not.
As for revelation in history, I don’t know what exactly is meant by that.

Does his “proof” for the existence of the revelation at Mount Sinai pass your test of criticism?

I don’t remember there being a proof there. The claim that there is a broad tradition about it carries some weight. But by itself it isn’t very strong. Within a broader overall framework it becomes more convincing. I explained this in The First Foundational Principle, fifth talk.
By the way, Shtenger is babbling himself to death there. It’s obvious he feeds on rumors and recites slogans (“we know…” with great certainty).

So I’ll copy here what Rabbi Sherki wrote in his article on Torah from Heaven: “One question deserves to be asked: how can one know that the entire biblical story was not invented? Here we must set out two basic principles. The first: every story about a foundational event of national identity is true. For example, how can one know that the French Revolution really took place? There is no need to travel to France and analyze historical documents. It is enough to see the impression the Revolution left on the French nation and on the entire Western world in order to be convinced that it happened. So too regarding the Holocaust: we do not believe that the Holocaust occurred only because we saw pictures or documents. The principal evidence for the occurrence of the Holocaust is the collective trauma that left its mark on the Jewish people. Anyone who looks at the Jewish people from the outside can understand that there was a Holocaust, because we behave like Holocaust victims. Let us qualify this rule and say that there are two kinds of foundational stories: there is a foundational story that deals with a period when the nation already exists, and there is a story that deals with a period prior to the nation’s formation. Only the first type of story is necessarily factual truth, because it is impossible to add to an entire nation a foundational story that did not happen. But the second type of story did not necessarily happen, because it could have been invented and afterward the belief in it strengthened by means of propaganda. For example, the myth of the founding of the city of Athens by the goddess Athena is an unfounded story, because it takes place outside Greek history. But the Trojan War certainly happened, because it is a foundational event that took place after the formation of the Greek nation. Therefore, if the Torah had been given to the Patriarchs and on that story we based belief in it, we could doubt the truth of the story, because the people of Israel had not yet appeared as a nation.
The second principle: a story that cannot be invented is true. This argument is brought in the portion of Va’etchanan (Deuteronomy 4:32): ‘For ask now of the days that are past, which were before you, since the day that God created man upon the earth, and from one end of heaven to the other, whether there has been anything as great as this, or has been heard like it.’ Scripture invites us to look at the stories of all peoples everywhere in the world and examine whether there has been or has been heard anything like this great thing. ‘Has there been’ means that it happened, that is, a true story. ‘Has been heard’ means that it is told, that is, that it did not happen. What is the content of the search? ‘Did ever a people hear the voice of God speaking out of the midst of the fire, as you have heard, and live?’ That is to say: you will search in vain for any tradition that speaks of a revelation of the Creator as a historical or mythological story. Such a story also cannot be invented, because the idea of the revelation of the Creator is foreign to the human soul. The thought that the Creator of everything would leave His transcendence and penetrate into reality in order to command man how to prepare Sabbath dishes is not a normative thought, and it does not even arise in the mind as fiction. Therefore there is no likelihood that an entire nation would speak about God’s revelation to it. Let us formulate it this way: the only people who even conceive of the idea that the Creator of the world speaks are those who say that He spoke with them—and from this it follows that they are telling the truth.
Examples:
Let us illustrate the argument with the following story: a small child who grew up in an entirely Hebrew-speaking environment comes home one day and says two sentences in Japanese. His parents ask him: who taught you those sentences? And he tells them that on the way home he met two people with slanted eyes and a big camera, and they said them to him. There is no possibility of not believing him, because there cannot be any other source for the child’s knowledge about those people and those sentences. There are lies that cannot be invented, and therefore they will not be told. So too regarding revelation: from prehistory until today there has been no culture that conceived of a story of the revelation of the Creator.
Pre-Socratic philosophy can serve as a fine example for our matter: all the philosophers in that period were pantheists in various ways and could not rise above the boundaries of the cosmos and recognize a distinct divinity. In certain mythological stories we do indeed find revelations of gods to human beings, but we are not speaking of a revelation of One who remains distinct and abstract; rather, of minor gods who are ultimately part of creation. Therefore, if there is an entire nation that says it experienced an encounter with the One who is beyond the world, it is necessarily telling the truth, because it could not have conceived this on its own.”
He also writes in a note to this article as follows: “It is also worth considering Christianity and Islam. The revelations to Jesus and Muhammad were never foundational stories of any nation. However, the place these religions occupy in human consciousness is so great that the stories about them certainly serve as a cornerstone of collective identity. But here we come to a fundamental difference from Judaism: the historical knowledge about the existence of Jesus and Muhammad does not teach of God’s revelation to Christians or Muslims, but only of the activity of Jesus and Muhammad themselves. If we ask Christians why they believe, their answer will ultimately be: we believe because we believe. If the people of Israel had accepted the Torah because of the figure of Moses our rabbi, there would have been no difference in the root of certainty. But the historical knowledge of the revelation at Mount Sinai, which left its impression on the Jewish people, contains within it the novelty of God’s revelation to a people, and in that way gives force to belief in Torah from Heaven.” End quote.
I’d be glad to know what the Rabbi thinks about this argument/proof.

This is copied from what he said by my typing it out, so there are probably a few inaccuracies in the wording (I couldn’t manage to copy-paste it).

It has some weight, but not at the level of certainty with which he presents it. You can also implant a public foundational story in a nation. There are many myths that deal with what happened to the people itself. So in my view these arguments do not stand on their own, and I explained this in the fifth talk of The First Foundational Principle, as mentioned above.

In your opinion, do the two assumptions he makes carry weight?

I wrote that they do.

Just out of curiosity, can you mention such myths that were implanted into a nation that already existed and that tell a story about that nation itself?

The Trojan War, for example.

Most researchers today think that a war at Troy really did take place, even if not exactly in the way described.

Let me add to the question: does the Rabbi know of an ancient myth of collective revelation?

No