Is it permissible to eat from an Udhiyah slaughtered on behalf of a deceased person?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to eat from the sacrifice (uḍḥiyyah) that is offered on behalf of a deceased person. This is the madhhab (school of thought) of the Hanbalis. In this case, the heirs take the place of the deceased as if he were alive, with the same rights to eat from it, give it in charity, and offer it as a gift.
It is stated in Maṭālib Uli al-Nuhā (Vol.2/P.472): "Offering a sacrifice on behalf of a deceased person is better than offering one on behalf of a living person, because the deceased is unable (to perform deeds) and is in need of reward. It is to be treated like a sacrifice on behalf of a living person in terms of eating, giving charity, and giving gifts." And Allah Almighty knows best.
Does tooth extraction during the day in Ramadan break the fast?
Simply extracting a tooth during the day in Ramadan does not break the fast. However, if water or blood enters the body cavity, the fast becomes invalid.
Whoever's fast is invalidated in this way must refrain from eating and drinking for the rest of the day out of respect for the sacred month and make up for that day later.
It is preferable to postpone the extraction until nighttime or after Ramadan if possible.
What are the pillars of fasting?
The pillars of fasting are intention and abstaining from all nullifiers of fasting from dawn to sunset.
Is it permissible to participate in an Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the sacrificial offering (Udhiyah), if it is a sheep or a goat, it only avails for one person. However, if it is a cow or a camel, it avails for seven people. It is permissible for the seven participants to have different intentions; for example, some may intend the sacrifice (Udhiyah), some the ’Aqiqah (sacrifice for a newborn), and others may simply intend to obtain meat.
It is stated in Hashiyat Qalyubi ‘ala Sharh al-Mahalli (Vol.4/P.256) and in Bushra al-Karim (p. 706):
"If one slaughters a camel or a cow on behalf of seven... it is permissible. Likewise, it is permissible if some of them intend their seventh for meat, and others intend their seventh for ’Aqiqah." And Allah the Almighty knows best.