Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
Which is superior: The Udhiyah (Sacrificial Offering) or giving its value in Charity (Sadaqah)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Performing the Udhiyah (sacrificial offering) is superior to giving its monetary value as charity (Sadaqah) to the poor and needy. This is because the Udhiyah is one of the manifest symbols of the religion. Allah the Almighty says {what means}: "That [is so]. And whoever honors the symbols of Allah - indeed, it is from the piety of hearts." [Al-Hajj/32]. This is further supported by the explicit and authentic Hadiths regarding its virtue, and the fact that the Prophet ﷺ and the Rightly Guided Caliphs after him consistently performed the sacrifice. And Allah the Exalted knows best.
Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
How should the sacrifice (udhiyah) be distributed?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to give the poor a portion of the meat from a voluntary sacrifice (Udhiyah al-Tatawwu’), which should not be less than approximately half a kilogram of raw meat. Other parts do not suffice for this obligation, such as the liver, tripe, or intestines.
It is Sunnah for the one offering the sacrifice to divide it into thirds: one-third for himself and his household to eat, one-third to be given as charity to the poor, and one-third to be given as a gift to friends and neighbors, even if they are wealthy. And Allah the Almighty knows best.