Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is it permissible for me to name my newborn baby boy “Al-Moustafa” ?
There is no harm in naming your son “Moustafa” without using the ”Al”.
I placed my hand on the Quran and made an oath to avoid doing a specific matter, but the devil seduced me. What is the ruling on this?
You are obliged to pay an expiation; feeding 10 poor and the cost of feeing one is half JD. And Allah Knows Best.
What is the ruling on a person who isn`t able to fast due to old age, or an incurable disease?
Paying the ransom is due on such a person, and that is giving a Mud (600 grams) of wheat, or rice, or the price of that amount to a needy Muslim for each missed fasting day. And Allah Knows Best.