Am I permitted to perform more than a prayer within single ablution?
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.
You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified. And Allah Knows Best.
My mother is 70 years old and wishes to perform Hajj and Umrah, as she has never done so before. However, she also takes care of my ill father and is afraid of falling ill herself. What should she do?
If this is the obligatory Hajj – meaning she has not previously performed Hajj or Umrah – then it is permissible for her to go even without her husband's approval. However, she must travel with a Mahram (a male guardian) or a trustworthy group of women, and she should leave someone to care for her husband and attend to his needs. And Allah Knows Best.
Is it permissible for a woman to swear a false oath by the Holy Quran to please her distrustful husband?
It is forbidden for a person to do so since this is considered a false oath (Yamaan Ghamoos) which dips (Yaghmos) its taker in Hellfire if he/she doesn`t seek repentance, and he/she has to expiate for that oath. You should avoid any doubtful acts so that your husband`s chest remains clear from the evil suggestions of the devil.
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.