Is it permissible for the mother to give her children from the Zakah (obligatory charity) of her money?
It is permissible for the mother to give her children from the Zakah of her money if they are Zakah-eligible recipients, and she isn`t obliged to provide for them.
What is the expiation for perjury?
One who commits perjury should repent, seek Allah`s forgiveness and offer an expiation which is: feeding ten indigent persons, or clothing them, or giving a slave his freedom, but if that is beyond his means then, he should fast for three days. Allah, The Almighty, Says in this regard (What means): "Allah will not call you to account for what is futile in your oaths, but He will call you to account for your deliberate oaths: for expiation, feed ten indigent persons, on a scale of the average for the food of your families; or clothe them; or give a slave his freedom. If that is beyond your means, fast for three days. That is the expiation for the oaths ye have sworn. But keep to your oaths. Thus doth Allah make clear to you His signs, that ye may be grateful." [Al-Ma`idah/89].
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.
What is the ruling on the follower (*maʾmūm*) reciting Sūrat al-Fātiḥah behind the imam?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
In our school of Islamic thought, the Shāfiʿī school, reciting al-Fātiḥah is obligatory in every rakʿah of the prayer for the imam, the follower (maʾmūm), and the one praying individually (munfarid), because it is one of the pillars (arkān) of the prayer. Whoever does not perform it, his prayer is invalid, whether the prayer is silent (sirriyyah) or audible (jahriyyah), based on the saying of the Prophet (peace and blessings be upon him): “The prayer of the one who does not recite the Opening of the Book (Fātiḥat al-Kitāb) is invalid.” Agreed upon.
It is stated in ʿUmdat al-Sālik, one of the books of the Shāfiʿī school: “He recites al-Fātiḥah in every rakʿah, whether he is the imam, the follower, or the individual worshipper.”
The jurists of the other schools hold a different opinion, which was previously explained in Fatwa no. (3169); please refer to it. And Allah Almighty knows best.