About this month’s menstruation

First, congratulations and best wishes. I hope and wish you a home full of happiness, wisdom, and joy.
Secondly, menstruation is indeed a problematic issue. I will first state that the Gemara in Yevamot 67b discusses various assumptions of three times (see in all this in Ka’bi Ta’arot 34 at great length), and two opinions are presented there regarding the question of whether an assumption is made even when there is no likelihood that there is a common cause for all cases (a chance cause or a kind of cause). But the poskim wrote that according to the law, there must always be at least a suspicion of some cause. See, for example, in Mekor Chaim O’H 377:

[5] And if they are not broken, etc. See Magen Avraham, 12: If three strong grains are found, it is good, and perhaps they are broken, and Magen Avraham conceals this, that we did not say so immediately, because I am not aware of it. And see Haqq Yaakov [25], which says that the hard grain is from the neighborhood of a cemetery [Nazir 64:2], etc. And in 17:17 we had to feel even in grains that contained three grains that had sprouted, and we felt that it was good, because it was kept, and testing was not necessary, because it had dried in the dry, and there was no spoilage, and so they had to test all of them. And even more, because there were three that had been fermented, it was good, because eating the grain in his eyes, even if it had not been broken, is forbidden.
Therefore, it seems to me that we should not say that there is a three-fold presumption unless, in this case, the cause is evident and the reason is compelling, it must be so. But in a matter that occurs by chance and in this case, the cause is evident, then there is no presumption for coincidences, and there is clear evidence for this from the Book of Proverbs [S”4 2], that in the case of a woman who is a murderer, there is no law for a murderer in her fiancée, and there is no law for a murderer in his husband, but in this case, there is a three-fold presumption. And there is further evidence from the 16th chapter of the Book of Leviticus, or the rules of the Torah or the rabbis, and the law is a three-fold presumption from the Torah, that one should go out in a special amulet for the public on Shabbat [Shabbat 61 1]. But therefore, there is no proof for a murderer or a cause that is evident. And because it is permissible to plant wheat on top of the wheat that has grown, there is no evidence that rains have fallen on those that have fallen, even though it is permissible, Daimer said, “He is a heap,” as the Maga wrote [16], section 5, in the name of the Rashba. And it is not difficult for Daimer to say that it is a denazir, since it is clear that it is a cemetery neighborhood, since they are placed from six to eight, and rather there is evidence from the words of Daimer that it is not a denazir. Even if there is no place from six to eight, it is a denazir, so that three dead people were buried there. It happened a lot more, but certainly one does not say the three-fold assumption except in something that is evidently the case. And in the 7th chapter, here, with wheat in a dish that fell by chance, we do not say the three-fold assumption, and according to the opinion of Magen Avraham, it seems clear to me:

It should be understood that suspicion does not mean something that is known to be a cause, otherwise it is not a presumption but medical information (a mass that falls to Earth does not do so because of a presumption but because it is known that there is a gravitational force). Suspicion always comes when there is something that is suspected to be a cause, meaning that it is possible that there is a cause, but it is not clearly known that it is one.
Therefore, at least the sages thought that there was probably a suspicion of a common cause for monthly menstruation. They may have been mistaken due to lack of knowledge (they had scientific and medical errors). But I once saw someone attribute it to the moon. If it causes tides, then it also has effects on the earth. Especially since humans also have psychology, and there is certainly room for explanation that people enter different moods on different dates of the month. And the psychophysical effect can cause physical phenomena.
Regarding halachic rulings, I am not knowledgeable about stains, but other questions can be asked and I will try to answer.
Congratulations again,