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 a Muslim woman to leave her house adorned and without wearing her proper Islamic attire?
A Muslim woman isn't permitted to leave her house adorned and without wearing proper Islamic attire. And Allah Knows Best.
Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?
It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.
My brother is settling a debt on my behalf and in return he takes 30% interest as an additional amount of the whole sum. Is this lawful or not?
This additional amount is considered prohibited interest (Riba) according to Islamic law, and it is not permissible to take it. And Allah Knows Best.
