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 Jumu‘ah (Friday) prayer for a traveler, and what are the conditions for it to be waived from him?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Jumu‘ah (Friday) prayer is not obligatory upon a traveler, whether on a long or short journey, provided that — according to the Shāfi‘ī school — he departs from his place of residence before the time for Fajr prayer begins, and that he does not intend to stay in the place he travels to for four days or more, excluding the day of arrival and the day of departure. If he intends to stay longer than that, he may not make use of the travel concession simply by arriving in that town. If he begins his journey after the adhān for Fajr has already been called, then Jumu‘ah prayer remains obligatory upon him, whether in his own town or in any town where Jumu‘ah is being held.
It is stated in Bushrā al-Karīm (Vol.1/p.383), from the books of the Shāfi‘ī school: "Jumu‘ah [prayer] is not obligatory upon a traveler on a permissible journey, whether long or short, if he departs from his place of residence before Fajr."
A "short journey" refers to travel covering a distance shorter than that of a long journey — that is, less than (81 km). The traveler begins to be entitled to travel concessions once he passes beyond the built-up limits of his town. And Allah, the Exalted, knows best.
What is the ruling on swearing a false oath by the Holy Quran?
Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.
What is the ruling of Islamic Law on shaving body hair and clipping the nails for one who is in a state of major ritual impurity (*junub*)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is recommended for one in a state of major ritual impurity (junub) not to remove anything from his body until after the ritual bath (ghusl). It is stated in Bushrā al-Karīm bi-Sharḥ Masāʾil al-Taʿlīm (p. 135): “It is recommended for one in a state of janābah and the like not to remove anything from his body until after ghusl, because the parts of the body return to him in the Hereafter, and he returns in a state of janābah, as a rebuke to him. Then it is removed from him, except for the original parts. It is said that every hair demands its due for its janābah.”
It is stated in Ḥāshiyat al-Shabrāmallisī ʿalā Nihāyat al-Muḥtāj (Vol.2/p.341): “If he wishes to combine shaving and the Friday ghusl, he should delay the shaving until after the ghusl if he is in a state of janābah, so that the ghusl removes its trace from the hair.” And Allah Almighty knows best.