Should one obey his mother even if she was wrong?
Obeying one`s mother is an obligation in matters that are beneficial to her and so long as she didn't drive her children to commit an act of sin.
What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.
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 taking a loan from an interest-based bank (a usurious bank) to buy an apartment for housing, noting that I am renting at a high amount relative to my income, and I am an employee? Also, considering that the conditions of Islamic banks are strict, and I cannot obtain the full amount from them, is it permissible to take a loan to purchase an apartment or not? May Allah reward you.
Usury (interest) is prohibited by Islamic law, and the Messenger of Allah, peace be upon him, cursed the one who consumes usury, the one who pays it, its recorder, and its witnesses. Whoever leaves something for the sake of Allah, Allah will compensate them with something better and greater, and Allah will provide relief after hardship. Needing a place to live does not permit taking a loan with interest. And Allah Knows Best.