Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.
Is it valid to perform the obligatory prayer while sitting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Standing (Al-Qiyam) while having the ability to do so is one of the pillars (Arkan) of the prayer; the obligatory (Faridah) prayer is not valid without it. However, whoever is unable to stand may pray sitting down. As for voluntary (Nafilah) prayers, it is permissible to pray them sitting even if one is able to stand, but the one sitting receives half the reward of the one who prays standing. And Allah the Exalted knows best.
What is the ruling on someone who fainted while fasting?
● If a person had the intention to fast from the night but then fainted during the day and regained consciousness before sunset, even for a moment, their fast remains valid.
● However, if they remain unconscious for the entire day, from Fajr until sunset, their fast does not count, and they must make up for that day later.