Do you have an example of a central or significant halakhic ruling that was nullified for these reasons?

Also, I’d be glad to know whether this also applies to health. I don’t know of such a Jewish law, but if a commandment were found, whether Torah-level or rabbinic, that causes shortening of life or is carcinogenic, God forbid, and the like (I don’t have examples right now), would it also be nullified even though people have been observing it all these years?

Absolutely. Killing a louse on the Sabbath, for example.
It doesn’t apply to health. What does that have to do with it? A Jewish law that carries health risks still has to be observed.

1. Is there no room to argue that the Jewish law is valid, and that the reasons the Sages gave are only an after-the-fact explanation? For example, regarding a louse on the Sabbath, perhaps killing it was permitted by tradition, and the Sages merely gave what they thought was the reason why it is permitted?

2. Also in the laws of tereifot, twilight, menstruation, and more, there are scientific errors, and despite this the Jewish law has hardly changed. Some of those errors would lead to uprooting entire commandments that are the basis of all religious life. Should Jewish laws be nullified even in such a case? And if so, where is the line drawn?

3. What about laws that the Sages tied to an ancient tradition, and science proved that no such tradition existed? For example, historical or archaeological sources that proved unequivocally that there was no such tradition, in a way that one cannot be persuaded otherwise (we are not talking about a reasonable possibility, but decisive evidence that anyone who hears it must accept).

1. Very unlikely. That is the Vilna Gaon’s thesis of hidden reasons. It is like saying that all the derashot are merely supportive. Apologetically, that is very convenient, and precisely because of that I’m suspicious of such claims. Usually, one should say about something that it is a law given to Moses at Sinai, and not tell me stories—and certainly not confusing and misleading stories that could lead me to mistaken conclusions.
2. The fact that the Jewish law has not changed is not something you can know. In practice, people do not act differently, but perhaps that conduct is mistaken? The claim is that the list of tereifot is a law given to Moses at Sinai. Maybe yes and maybe no, but whoever claims yes bears the burden of proof. And if these errors really are errors, they should be uprooted with a strong hand and an outstretched arm. And if that leads to uprooting whole commandments—that is one of the positive consequences. I have no interest whatsoever in clinging to mistaken commandments. There is no line. Or rather: the line is drawn exactly at the line of truth.
3. Here I need an example.

1. In the case of supportive derashot that are Torah-level according to all opinions, can one argue this? That is, the derashah is a kind of asmakhta, and perhaps there is an ancient tradition? And what about Torah-level laws that relied on mistaken science (and were not learned from the hermeneutical principles)? There too, can one not argue that the Sages merely gave an after-the-fact reason?

2. If so, then many laws of tereifot, the laws of menstruation, and twilight are no longer relevant, because it is clear that they are based on mistaken science. Today it is known that wolves do not have venom in their claws, and therefore they do not render an animal a tereifah. The rest of the kosher laws are also nullified, since there are no worms generated from the earth. The laws of menstruation are also not relevant, because the Sages erred in anatomy and in the source of the blood, and it is known that there is no difference between blood from a wound and menstrual blood. In practice, it may be that there is no Torah-level impurity of menstruation at all, and this is like the wayward city or the stubborn and rebellious son.
Also in additional laws like ritual slaughter there are errors. If so, it turns out that most Jewish law nowadays requires change or is not relevant.
From looking through the site, I haven’t seen the Rabbi calling to abolish these commandments.

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

The researcher here argues that in the biblical period there was no immersion. I haven’t studied the matter in depth, but if it turns out unequivocally that there were no immersion pools in the biblical period, that would nullify all the Sages’ laws of mikva’ot, and in practice the overwhelming majority of the laws of purity and impurity, since the impure remain impure because they are not purified properly.
There are midrashim about immersion in early periods before the appearance of mikva’ot, according to the researcher. What should be done in such a case?
Should we nullify the words of the Sages because they were based on a mistaken tradition, or accept the words of the Sages because they have authority to change things?

1. I didn’t understand the question. In supportive derashot, the Jewish law is not based on the derashah, so you cannot know whether it is mistaken or not. Do you mean to ask what we do when the derashah is based on an error? If it is a supportive derashah, then you are right: even if the derashah is mistaken, that does not nullify the law. But you need proof that this is a supportive derashah, because almost all derashot are creative ones (as Maimonides wrote, all except “about three or four”).
What did you mean by Torah-level laws that rely on mistaken science? Creative derashot based on an error? Their conclusion is of course nullified. The fact that the law is classified as Torah-level changes nothing. It is the handiwork of the Sages, and if it was created in error, it is nullified.
2. Indeed, once it becomes clear that this is a scientific error, and it becomes clear that the law is based on it, it is nullified. I wrote that. Each example has to be judged on its own merits. In some of the examples you brought, your conclusion is really not necessary, but this is not the place to get into the details of the examples (and I am not expert in some of them either).
3. Why would that change anything? If there was no immersion, that means immersion was introduced later. There are Torah-level laws that came into being over the generations, and they are binding just like the laws from Sinai. In fact, most Torah-level laws are products of creative derashot or interpretation, so there is no obstacle to their having been created over the generations. What is the problem with that? As for immersion, it is almost explicit in Sabbath 64 in Rabbi Akiva’s derashah against what the earlier generations practiced, that a menstruating woman should not put on eye paint or rouge during her state of menstruation. Then Rabbi Akiva came and expounded: until she enters the water.