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.
Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Is it permissible for a woman to lead other women in prayer?
Yes, it is permissible for a woman to lead other women in prayer. The most knowledgeable among them in the rulings of prayer should act as the imam. She should stand in the middle of the row, slightly ahead of the others.