Is it permissible to give Zakah (obligatory charity) to one`s poor sister, or brother?
It is permissible for one to give the Zakah to his poor sister, or brother if providing for them isn`t due on him, and the sister doesn`t receive sufficient provision from whomever that is due on. And Allah Knows Best.
What is the ruling on offering an Udhiyah on behalf of another with their permission?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for a person to offer a sacrifice (Udhiyah) on behalf of someone else with their permission, even if the person performing it has not offered a sacrifice for themselves. It is stated in Sharh Manhaj al-Tullab (Vol.5/P.261) by Zakariya al-Ansari: "No one may offer a sacrifice on behalf of another without their permission... as opposed to when permission has been granted." And Allah the Almighty 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].
What is the ruling on performing dry ablution (tayammum) instead of the ritual bath due to severe cold?
Whoever is sick such that he cannot use water, or finds the water cold and heating it is not possible, and the person would be harmed by using cold water, it is permissible for him to perform tayammum. He must make up what he prayed with tayammum, because this is a place where there is water. And Allah the Almighty knows best.