And what would the law be if he is in doubt whether it was given at Mount Sinai? And he observes on the assumption that it indeed was given there? (This is no longer connected to authority from below, sorry.)

That seems totally fine to me. In fact, every person is like that, since after all no one can be certain.

I didn’t understand how the Rabbi infers this from there. Could you explain?

Are you talking about Maimonides? It says so there. I don’t know what you want me to explain.

Moses our Rabbi gave the Torah and the commandments as an inheritance only to Israel, as it says, “an inheritance of the congregation of Jacob,” and to anyone from the other nations who wishes to convert, as it says, “as you are, so shall the stranger be.” But one who does not wish to do so is not compelled to accept Torah and commandments. And so Moses our Rabbi, by the command of the Almighty, commanded to compel all the inhabitants of the world to accept the commandments that the descendants of Noah were commanded; and anyone who will not accept them is to be killed. One who accepts them is called a resident alien everywhere, and he must accept them before three associates. And anyone who accepted upon himself to be circumcised, and twelve months passed and he was not circumcised, is regarded as one of the nations.

Law 11
Edit
Anyone who accepts the seven commandments and is careful to observe them is among the pious of the nations of the world and has a share in the World to Come—provided that he accepts and observes them because the Holy One, blessed be He, commanded them in the Torah and informed us through Moses our Rabbi that the descendants of Noah had already been commanded regarding them. But if he observed them because reason convinced him, he is not a resident alien and is not among the pious of the nations of the world, nor of their wise men.
What does this have to do with the question?

Ah, good that you quoted it. Now everything is clear. Now you can see, like the rest of us, that it is simply written there and no explanation is needed. What needs explaining when Maimonides writes that one must observe commandments because of the command and not for some other reason (the dictate of reason)?

First of all, Maimonides only distinguishes between the pious of the nations of the world and their wise men, and does not necessarily say anything about Jews.
Second, the question was not about the dictate of reason or because of the command, but about someone who acts because he believes in God, just not that He actually commanded it; rather, he does what his people undertook as the way to serve God. That is not the dictate of reason and not because of the command.

The same applies with respect to Jews. That is simple logic. See in the Frankel index there that the later authorities wrote this explicitly (if I recall correctly, there is one who did not write this way, and his words are puzzling).
Everything else is just reading comprehension. I’m done.

All right, thanks for taking the time.