Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.
If a woman becomes pure from menstruation shortly after Fajr in Ramadan, what is required of her?
If a woman becomes pure (from menstrual period) after Fajr, even shortly after, it is recommended (but not obligatory) for her to refrain from eating and drinking for the rest of the day. However, she must make up for that day after Ramadan.
She will be rewarded for both refraining from eating (imsak) and making up the fast (qada) since she was menstruating for part of the day.
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.
What is required of one who doubts the number of rakʿāt during prayer?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If a person doubts the number of rakʿāt he has prayed, he should build upon the lesser number, as that is what he is certain of. He should then perform the prostration of forgetfulness (sujūd al-sahw) before the final salām at the end of the prayer. ʿAṭāʾ ibn Yasār narrated that the Messenger of Allah ﷺ said: "When any one of you is in doubt during his prayer and does not know whether he has prayed three rakʿāt or four, let him pray one more rakʿah and then perform two prostrations while seated before the salām. If the rakʿah he prayed was a fifth, these two prostrations will make it even; and if it was the fourth, then the two prostrations serve as a humiliation for the devil." (Reported by Abū Dāwūd.)
It is stated in al-Muqaddimah al-Ḥaḍramiyyah — one of the foundational texts of the Shāfiʿī school: "If one doubts whether he has prayed three rakʿāt or four, he is obliged to build upon the lesser number."
However, if such doubt recurs repeatedly and reaches the level of obsessive whispering (waswasah), he should not build upon the lesser number in that case — rather, he should build upon the greater number. And Allah the Almighty knows best.
