All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
There is no doubt that Allaah, The Exalted, has decreed that women would experience menstruation. The Prophet, sallallaahu ‘alayhi wa sallam, said: “This is a matter which Allaah has decreed for all the daughters of Aadam.” [Al-Bukhari] The wisdom behind that was underlined by Ibn Qudaamah as he wrote, “The wisdom behind (decreeing that women would experience) menstruation is that the fetus is nurtured by it during pregnancy. So, a woman who is not eligible for pregnancy is not eligible to menstruation.” [Al-Mughni]
It should be noted that the Islamic Sharee‘ah does not oblige the woman to do any of what you have mentioned in the question, nor does it direct Muslims to treat women like aliens during menstruation. Unlike the practice of Judaism, Islam deems it allowable to eat and sit with menstruating women, and even allows the husband to enjoy his menstruating wife without sexual penetration.
Nevertheless, if this woman’s reaction is (done) out of her modesty and bashfulness, this is commendable. Verily, bashfulness does not bring about anything but good. Some scholars recommended that the menstruating woman should eat and drink in secret during fast days of Ramadan and hide her non-observance of fast in Ramadan from those who do not know her excuse so that people would not think ill of her and assume that she is lax about observing religious obligations. For further information, please refer to Fatwa 86651.
It is quite clear that she should eat and drink in secret during the fast days (of Ramadan) in order to avoid people’s suspicions (that she deliberately eats and drinks in the fast days of Ramadan with no excuse). Therefore, she is not obliged to eat and drink secretly and hide her condition from those who already know about her excuse.
For more benefit, please refer to Fatwa 86795.
Allaah Knows best.