Is it permissible for a woman who is observing `Iddah (waiting period) due to the death of her husband to travel for performing Umrah (Minor Hajj)?
A woman observing `Iddah of a revocable (Rajee`) divorce isn`t allowed to travel for Umrah except with the consent of her husband.
Is the Aqeeqa due on the newborn in case of dying almost a month after the delivery?
Offering Aqeeqa after a week of a newborn death is recommended.
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.
Is Making up Missed Obligatory Prayers an Obligation?
All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Missed obligatory prayer/prayers is a debt upon Muslim and making it up is an obligation, since the Prophet (PBUH) said: "pay the debt due to God, for it is the one which most deserves to be paid." [Agreed upon]. And Allah Knows Best.