Can a woman leading other women in Tarawih prayer recite aloud?
Yes, a woman leading other women in Tarawih prayer is allowed to recite aloud, as long as no non-mahram (other than unmarriageable kin) men can hear her.
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 ruling of Islamic Law on eating or drinking forgetfully while observing the kaffarah fasting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If someone eats or drinks out of forgetfulness while fasting, it is simply that Allah has fed them and given them drink. Their fast is not broken by this; rather, they should continue fasting. This ruling applies whether the fast is an obligatory one (like Ramadan), a make-up fast (Qada), an expiation (Kaffarah), or a voluntary (Nafal) fast. And Allah the Exalted knows best.
What should a person do if they suffer from an incurable illness that prevents them from fasting?
A person who has an illness that is not expected to be cured and prevents them from fasting must feed a needy person one mudd (600 grams) of food (such as wheat or rice) for each missed day instead of fasting.
Allah Almighty says {what means}: "and [in such cases] it is incumbent upon those who can afford it to make sacrifice by feeding a needy person." [Al-Baqarah/184].