Is the woman who do breastfeeding permitted to break the fast during Ramadan?
It is permissible for pregnant and breastfeeding women to break their fast during Ramadan if they fear harm to themselves or their child. However, they must make up for the missed fasts. If the fast is broken out of concern for the fetus or the baby, expiation (Fidya) is also required along with making up the missed fasts. The expiation involves feeding one needy person with an amount equivalent to a Mudd of food (approximately 600 grams of wheat or rice) for each day of missed fasts. If the fast is broken out of concern for the woman's own health, only making up missed fasts is obligatory. And Allah Knows Best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
What is the ruling on reciting verses from the Qur'an over water, drinking it, and using it to break magic spells, heal illnesses, or burn jinn?
There is no harm on reciting verses of the Holy Qur'an over water and use it for cure. And Allah Knows Best.
What is teh ruling on thoughtless oath?
One who swears by Allah unintentionally and isn`t determined to fulfill his oath, nothing is due on him. Allah, The Almighty, Says (What means): "God will not call you to account for thoughtlessness in your oaths, but for the intention in your hearts; and He is Oft-forgiving, Most Forbearing." [Al-Baqarah/225]. However, it is dispraised for a Muslim to swear frequently.