After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.
After buying tires, I made an oath not to buy tires from a person. Afterwards, he offered his entire car for sale. What is the ruling on this?
If you bought the entire car and in order to be on the safe side, you should pay an expiation; feeding 10 poor people and the cost of feeding a person is half a JD. 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.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.