Mdd, it’s in the rema in toras ha’olah cited earlier, maharal on beer hagolah, aruch hashulchan,maharsha in beginning of mi she’ochzu spells it out very clearly.
Re, niddah; like i said earlier, the mesorah is clear that we don’t ignore chazal and we don’t ignore science; gedolim have been reconciling chazal snd science for millenia. I’m not familiar with that particular gemara, but i can give many such examples, such as kinnim, where rav belsky explained that “coming from sweat” refers to the scientific fact that of all egg-laying species, only lice rely on outside materials to nurture the larvae. Just as worms that grow inside a fish are considered fish, since that’s all that they’ve eaten, so too lice are considered “sweat” because that’s how they derived the nutrients necessary to hatch.
So not only did chazal not contradict science, their statement shows a deep knowledge well beyond their era. Rav belsky had many, many such examples, but this approach is rooted in rishonim and achronim across the board.
If you want chazals which say that they knew all there is to know about science, there’s a statement about Shmuel knowing “shvilei derakiah” from the Torah, pesukim darshened for things like the gestation period of a snake…
Also see what i wrote above from rav chaim volozhiner about the gra’s knowledge of the scientific world, where he understood the nature of every limb of every aninal from one phat in one pasuk. Rav chaim also writes that the gaon once said that he could show philosophers all of creation and make them be machniah themselves to the chachmas hatorah.