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.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
Are school exams a valid excuse for breaking the fast in Ramadan?
School and university exams are not considered a valid excuse for breaking the fast, as most students take their exams while fasting without experiencing extreme hardship. Fasting does not conflict with exam preparation, and a Muslim seeks strength in obedience to Allah for both worldly and spiritual matters.
Is it permissible to give to the poor from among the People of the Book from the Udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to give to the poor among the People of the Book from a voluntary sacrifice (uḍḥiyyat taṭawwuʿ), just as it is permissible to give charity (ṣadaqah) to them. This opinion is a view (wajh) within the Shāfiʿī school, which was favored by al-Muḥibb al-Ṭabarī and Imam al-Nawawī. [See: Ḥāshiyat Ibn Qāsim al-ʿAbbādī ʿalā Tuḥfat al-Muḥtāj (Vol.9/P.365)]. And Allah Almighty knows best.