Who is the one required to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered by the guardian of the newborn — the one upon whom the child's financial maintenance is obligatory — provided he is financially capable of doing so. 'Alī ibn Abī Ṭālib, may Allah be pleased with him, reported: "The Messenger of Allah ﷺ performed the 'aqīqah for al-Ḥasan with one sheep." — Narrated by al-Tirmidhī. And Allah Almighty knows best.
In the Sharia-compliant viewing at a prospective bride (*al-naẓrah al-sharʿiyyah*), is it permissible for the man to see the woman without a veil (*ḥijāb*)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is sunnah for the suitor to see the woman he is seeking to marry within the limits the Sharīʿah permits, namely looking at the face and the hands (palms and backs), based on the saying of the Prophet (peace and blessings be upon him): “Look at her, for it is more likely to bring about harmony between you.” Narrated by al-Tirmidhī.
The suitor may also ask one of the women to look at the woman he is seeking to marry. In that case, she is permitted to see of her what she is normally permitted to see, which is not limited to the face and hands, and she then describes these matters to the suitor. It is narrated on the authority of Anas (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) sent Umm Sulaym to look at a girl, and said: “Smell her breath, and look at her heels.” Narrated by Aḥmad in his Musnad.
It is stated in Tuḥfat al-Muḥtāj (Vol.7/p.192): “For one who cannot easily look, or does not wish to look himself, it is sunnah to send someone who is permitted to look at her, to observe her and describe her to him, even regarding what he himself is not permitted to look at. He thereby gains through the sending what he would not gain through looking. Because of the added need for this, it is excepted from the prohibition of a woman describing another woman to a man.”
The permissibility of looking is conditional upon his resolve to marry her once he is able to, his predominant assumption that his proposal will be accepted, and his assumption that the woman is free of marriage and of a waiting period (ʿiddah). Otherwise, looking is forbidden.
Accordingly, it is not permissible for the suitor to look at anything other than the face and hands. He may ask one of his maḥram women, such as his mother or sister, to see the woman unveiled, and the Sharia-compliant viewing (of a prospective bride) must take place in the presence of one of the woman’s maḥrams. And Allah Almighty knows best.
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.
Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.