Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
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 it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
Ruling when Husband Utters Divorce Jokingly, or in the State of Intoxication or Anger
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The man who utters divorce while in the state of anger, his divorce doesn`t take place and the same ruling applies to the man who is forced to utter divorce because he is threatened to be killed or one of his organs cut off, in addition to other matters that scholars have mentioned in this regard. However, the man who utters divorce jokingly or while having intentionally drunk alcohol, his divorce takes place. And Allah The Almighty Knows Best.