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.
Should a prayer performer who forgets to offer the middle Tashahod (saying ash-hadu anala ilaha ila-alah) offer Sujood As-Sahw (prostration of forgetfulness)?
He/she should offer two prostrations of forgetfulness at the end of the prayer. And Allah Knows Best.
What is the ruling on fasting?
Fasting in Ramadan is an individual obligation (Fard ‘Ayn) upon every mature, sane Muslim who is capable of fasting.
Fasting can also be recommended (Mustahabb), such as voluntary fasting on Mondays and Thursdays, fasting on the Day of Arafah for those not performing Hajj, and fasting on Ashura.
Fasting can be prohibited (Haram), such as fasting on the two Eid days, the Day of Doubt (Yawm al-Shakk), and the Days of Tashreeq.
Some types of fasting are disliked (Makruh), such as singling out Friday or Saturday for fasting without a specific reason and fasting on the Day of Arafah for a pilgrim.
Is it permissible to include others in the reward of one`s sacrifice?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible for the one offering a sacrifice (al-muḍaḥḥī) to include another person in the reward of the sacrifice, but it is not permissible for them to share in the price of the sacrifice. It is stated in Mughnī al-Muḥtāj (Vol.6/P.137) by al-Khaṭīb al-Shirbīnī: "If he includes another in the reward of his sacrifice and slaughters it on his own behalf, it is permissible." And Allah Almighty knows best.