Halachic axioms that change over the generations

Do you have an example of a central or significant halakha that was invalidated by these circumstances?

I would also like to know if this also applies to health. I am not familiar with such a law, but if a mitzvah is found, from the Torah or from the Rabbis, that shortens life or causes cancer, God forbid, etc. (I don't have any examples right now), will it also be invalid even though it has been observed all these years?

Absolutely. Killing a louse on Shabbat, for example.
Not valid regarding health. What does this have to do with it? A rule that arises in health must be observed.

1. There is no reason to believe that the halacha is valid and that the reasons that Chazal gave are only an explanation after the fact? For example, killing a mite on Shabbat was permissible according to tradition, and Chazal only gave a reason in their opinion why it is permissible?

2. Even in the laws of tripot, between the suns, niddah, and more, there are scientific errors, and despite this, the halacha has hardly changed. Some of the errors will result in the displacement of complete commandments that are the basis of all religious life. Should the laws also be annulled in such a case? And if so, where does the line cross?

3. What about the laws that Chazal planted in ancient tradition and science has proven that there is no such tradition? For example, historical or archaeological sources that unequivocally proved that there was no such tradition in a way that cannot be convinced otherwise (this is not a reasonable possibility, but unequivocal evidence that whoever hears them must accept).

1. Very unlikely. This is the thesis of the hidden reasons of the rabbi. It's like saying that all sermons are reliable. Apologetically, it's very convenient, and that's precisely why I'm suspicious of these statements. Usually, one is supposed to speak about something that is the LBM and not tell me stories, and certainly not confusing and misleading stories (that might lead me to wrong conclusions).
2. You can't know that the halakha hasn't changed. In practice, they don't practice differently, but maybe this behavior is wrong? The claim is that the list of trifet is the LBM. Maybe so, maybe not, the one who claims so has the burden of proof. And if these errors are errors, they must be uprooted with a strong hand and an outstretched arm. And if this leads to the uprooting of the commandments of completeness - this is one of the positive consequences. I have no interest in clinging to wrong commandments. There is no limit. Or rather: the border runs exactly along the line of truth.
3. Here I need an example.

1. In authoritative sermons that are Torah according to all opinions, can we believe this? That is, the sermon is a type of reference and there may be an ancient tradition? And what about the laws of Torah that relied on incorrect science (and were not learned from the Proverbs)? There, it cannot be believed that the rabbis only provided a reason in retrospect?

2. If so, many laws of treptophobia, the laws of Nida and Bin Shemesh are no longer relevant because they are clearly based on incorrect science. Today, it is known that wolves do not have venom in their claws and therefore do not drive mad. The rest of the laws of kashrut are also invalid, since there are no worms that emerge from the ground. The laws of Nida are also irrelevant because the rabbis were wrong about the anatomy and the source of the blood, and it is known that there is no difference between the blood of a blow and menstrual blood. In fact, it is possible that there is no impurity of Nida from Torah, and this is like a remote city or a rebellious and disobedient son.
There are also errors in other laws, such as slaughter. If so, it follows that most of the rabbis today need to be changed or are irrelevant.
From a review of the website, I did not see that the rabbi calls for the abolition of these commandments.

3. For example, this.
https://www.thetorah.com/article/biblical-purification-was-it-immersion

The researcher here claims that there was no immersion in biblical times. I have not investigated the matter in depth, but if it is unequivocally proven that there were no immersion pits in biblical times, this would nullify all of the laws of impurity and purity of the Sages, and in fact the vast majority of the laws of impurity and purity, since the impure remain in their impurity because they are not purified properly.
There are midrashim on immersion in ancient times before the appearance of mikvahs, according to the researcher. What should be done in such a case?
Should the words of the Sages be annulled because they were based on a false tradition, or should the words of the Sages be accepted because they have the authority to change.

1. I didn't understand the question. In authoritative sermons, the law is not based on a sermon, so you can't tell if it's wrong or not. Do you mean to ask what to do when the sermon is based on an error? If it's an authoritative sermon, then you're right. Even if the sermon is wrong, it doesn't invalidate the law. But you need evidence that it's an authoritative sermon because almost all sermons are creative (like Maimonides, all except three or four).
What did you mean by the Torah laws that are based on incorrect science? Creative sermons that are based on an error? Their conclusion is of course invalid. The fact that the law is classified as Torah law changes nothing. It is the work of the sages, and if it was created by mistake, it is invalid.
2. Indeed, once it turns out to be a scientific error and it turns out that the law is based on it, it is invalid. I wrote that. Every example is a body. In some of the examples you gave, your conclusion is really not necessary, but this is not the place to go into the details of the examples (and I am not familiar with some of them either).
3. Why does it matter? If there was no immersion, it means that immersion was renewed later. There are laws from the Torah that were renewed throughout the generations and they are as binding as the laws that I have written. In fact, most laws from the Torah are products of creative sermons or interpretations, and therefore there is no prohibition that were created throughout the generations. What is the problem with this? Regarding immersion, it is almost explicitly stated on Shabbat 12 in the sermon of the Rebbe against what the first generations practiced, that you should not wash or fold your hands in the water. Then the Rebbe came and preached until you come into the water.