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.
What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.
Is it permissible for a guardian (Big brother) to unlawfully stop his sister from getting married?
If the guardian denies her right in getting married for an unlawful reason, she should go to court in order to settle that matter, and the guardian is considered sinful in this case.
Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.