Is it permissible to eat from an Udhiyah slaughtered on behalf of a deceased person?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to eat from the sacrifice (uḍḥiyyah) that is offered on behalf of a deceased person. This is the madhhab (school of thought) of the Hanbalis. In this case, the heirs take the place of the deceased as if he were alive, with the same rights to eat from it, give it in charity, and offer it as a gift.
It is stated in Maṭālib Uli al-Nuhā (Vol.2/P.472): "Offering a sacrifice on behalf of a deceased person is better than offering one on behalf of a living person, because the deceased is unable (to perform deeds) and is in need of reward. It is to be treated like a sacrifice on behalf of a living person in terms of eating, giving charity, and giving gifts." And Allah Almighty knows best.
Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.
What is the Islamic ruling on the Udhiyah (sacrificial offfering)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The Udhiyah (sacrificial offering) is a Confirmed Sunnah (Sunnah Mu’akkadah) for every adult Muslim of sound mind who possesses the financial means, whether they are a resident, a traveler, or a pilgrim (Haj). This is based on the statement of the Prophet ﷺ: 'When the ten days [of Dhu al-Hijjah] begin and one of you desires to offer a sacrifice, let him not touch [cut] anything of his hair or skin' [Narrated by Muslim].
The point of evidence (Wajh al-Dalalah) here is that the Prophet ﷺ linked the sacrifice to the individual's will and desire by saying, 'and one of you desires.' This indicates that it is not obligatory (Wajib); had it been mandatory, he would have simply said, 'let him not touch his hair until he sacrifices' [without making it conditional upon desire].
Furthermore, it is narrated that Abu Bakr and Umar (may Allah be pleased with them both) would sometimes refrain from offering the sacrifice out of fear that people might mistakenly view it as an obligatory duty [Narrated by al-Bayhaqi and others with a good (Hasan) chain of transmission]. And Allah the Exalted knows best.
What is the waiting period ('Iddah) for a woman whose husband has passed away, and what is the ruling on her wearing gold?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The waiting period ('Iddah) for a woman whose husband has passed away is four months and ten days for one who is not pregnant. As for a pregnant woman, her waiting period lasts until she gives birth. It is obligatory for her to remain in the marital home, only leaving for a necessity. During this time, it is prohibited (Haram) to display any form of adornment on the body or clothing; this includes wearing kohl, gold, all types of perfume, and dyeing the hair. Likewise, it is prohibited to receive a direct marriage proposal or to marry during this period.
It was narrated by Umm 'Atiyyah that the Prophet ﷺ said: 'We were forbidden to mourn for a deceased person for more than three days, except for a husband, for whom the mourning period is four months and ten days. During this time, we were not to use kohl, nor wear perfume, nor wear dyed clothing except for garments made of 'Asb (coarsely dyed yarn). We were, however, granted a concession at the time of purification—when one of us bathed following her menses—to use a small amount of Kust (costus) or Azfar (fragrant substances). We were also forbidden from following funeral processions.' (Narrated by Al-Bukhari). And Allah the Exalted knows best."