Why, for example, is the Talmud yes, but the medieval authorities are not? And what if we disagree with them and are certain that our claim is correct?

Because we accepted the Talmud upon ourselves (see Kesef Mishneh, beginning of chapter 2 of the Laws of Rebels)

With all due respect, Rabbi, Maimonides in the Laws of Rebels chapter 1 says that this is referring to the Great Court in Jerusalem… not to other sages!
From his words there you can see that he really distinguishes between the hermeneutical principles by which the Torah is expounded and the Oral Torah, even though you have said many times that the Oral Torah was very small and only laws and a few halakhot given to Moses at Sinai were stated in it!
And he emphasizes there that what is received by tradition relies on derivation through those principles…
In halakhah 9 it is written: If two sages or two courts disagreed at a time when there was no Sanhedrin, and before the matter had come before them—whether in the same generation or one after the other—one declared impure and one declared pure, one prohibited and one permitted: if you do not know which way the law inclines—regarding Torah law, follow the stringent opinion; regarding matters of the Sages, follow the lenient opinion. End quote.
Do you not see with your own eyes how he separates actual Torah law from rabbinic law! It seems he does not admit that this is genuine tradition and that things changed! Is that what happened in the dispute between Rabbi Eliezer and the Sages? One declares impure and the many declare pure!

I ask the Rabbi: would it not have been better if the laws had been given from the outset and not hidden? What is the reason for hiding them from the entire nation? And then passing the laws on through tradition, which also did not preserve itself—see that in Maimonides’ own manuscript he wrote that disputes multiplied in Israel… What caused the abolition of the Great Court, and why did they not appoint replacements for them in secret?

Moshe. If you want an answer to something, you need to explain the question better. This jumble of fragmentary quotations says nothing to me. Please, briefly and clearly. Thanks.

It takes knowledge and discernment to ask halakhic questions properly. Indeed.

From what I expanded on above, explained, and quoted, I will extract my questions:
1. I ask the Rabbi: would it not have been better if the laws for studying the Torah, which are written in the Oral Torah, had been given from the outset and not hidden?
2. And since that is how it was done (given orally), it was forbidden to write them down—what is the reason for hiding them from the entire nation? And then passing the laws on through tradition, which also did not preserve itself.

3. See that in Maimonides’ own manuscript he wrote that disputes multiplied in Israel—(following the abolition of the Great Court). What caused the abolition of the Great Court, and why did they not appoint replacements for them (even secretly, without the gentiles knowing about it) in secret?
4. Why nowadays is there no Great Court that would decide for all the communities, and not just some large religious court without authority, so that all disputes would be erased and completely uprooted—like the court that existed during the Second Temple period.

1. A text never contains the rules for its own interpretation. Those always accompany the text. Even if the Torah had included an appendix with a list of hermeneutical rules, that would not have helped. Their application would have aroused the same disputes anyway (as indeed happens in practice). Even in a Hebrew book, when the word “mountain” appears, it does not say next to it, or in an appendix dictionary, what the word means. The assumption is that people know the language and its rules of interpretation.
2. The prohibition against writing was not meant to conceal, but to keep matters open and not fixed. That is the nature of the Oral Torah: it is interpreted according to the circumstances.
3. Maimonides’ source is the Talmud. But it was not because of the abolition of the Great Court; rather, it was because forgetfulness increased among the students of Hillel and Shammai, who had not attended their teachers sufficiently. There were decrees against ordination, and in addition, according to Jewish law there is no ordination outside the Land of Israel, so in the end they were unable to ordain. Rabbi Yehuda ben Bava died over having ordained five students.
4. Because of what I wrote in 3. Beyond that, I do not see the abolition of disputes as such a great ideal.