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.
What is the ruling on waiving a debt owed by a debtor and counting it toward zakāh?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Waiving a debt owed by a debtor, with the intention of counting it toward zakāh, does not fulfill the zakāh obligation. Rather, it constitutes an ordinary act of charity, for which Allah rewards the giver generously — since one of the conditions for the validity of zakāh is that the person paying it must form the intention of zakāh at the actual moment the wealth is paid out. In this case, the debt has already been established as a standing obligation upon the borrower, so it is not valid to simply redirect the intention toward zakāh after the fact.
It is preferable, instead, for the creditor to first collect the debt from the debtor, and then return to him the amount of money he is required to pay as zakāh — or a portion of it — if the debtor happens to fall under one of the eight categories that Allah, the Exalted, has commanded be given from zakāh.
It is stated in ‘Umdat as-Sālik, from the books of the Shāfi‘ī school: "If someone gives [money] to a poor person, stipulating that the recipient return it to him in payment of a debt owed to him, or says, 'I am making what you owe me into zakāh, so take it [as such]' — this is not valid. But if he gives it to him with the [unstated] intention that the recipient will use it to repay him, or says, 'Repay what you owe me, so that I may [then separately] give it to you as zakāh,' or the debtor himself says, 'Give it to me, so that I may [then] repay you with it' — this is valid, and there is no binding obligation for the recipient to actually fulfill this [informal understanding]." And Allah, the Exalted, knows best.
Is it correct that everything dry is pure even if it has impurity on it?
If something impure becomes dry, it remains impure and is not purified by drying. However, the impurity does not transfer by touching it if the one touching it is also dry. And Allah the Almighty knows best.
A woman made a wig for herself from her own [previously shed] hair, which she wears on her head after having lost her hair [due to hair loss]. Is this permissible?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Since the hair belongs to the woman herself, the wig can be removed during the obligatory ghusl (ritual bathing), and part of the head can still be wiped during wuḍū' (ablution), there is no sharī‘ah objection to making this wig — provided she does not appear wearing it in front of non-maḥram men (Any males outside a woman's immediate family whom she is permitted to marry under Islamic law), since it is not permissible for them to look at a woman's detached hair.
It is stated in Rawḍat aṭ-Ṭālibīn wa ‘Umdat al-Muftīn: "Whatever it is not permissible to look at while still attached [to the body] — such as the male genitalia, a free woman's forearm, the hair of her head, and a man's pubic hair, and similar matters — it remains unlawful to look at even after it has been detached [from the body], according to the more correct position (al-aṣaḥḥ)." And Allah, the Exalted, knows best.