Someone asked me to pay off his debt on his behalf as a loan, without any compensation. When I went to the creditor, he told me that if I paid the full amount at once, rather than in installments, he would give me a certain discount. Is this permissible? And if he applies the discount, to whom does the deducted amount belong?

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.

What is the ruling on a man leading his sisters in obligatory prayer, or Taraweeh prayer (Night prayer in Ramadan)?

The prayer of the man who leads his wife, or sisters in prayer is valid, but it is more rewarding for him to offer obligatory prayer in the mosque. And Allah Knows Best.

Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?

Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.