What are the categories of the livestock permissible for Udhiyah?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
An Udhiyah (sacrificial offering) is only valid if it is selected from Al-An'am (livestock), which includes: camels, cattle, and sheep or goats—whether male or female, and even if castrated. Allah Almighty says {what means}: "And for all religion We have appointed a rite [of sacrifice] that they may mention the name of Allah over what He has provided for them of [sacrificial] livestock." (Al-Hajj/ 34)
In terms of preference, camels are considered the best choice, followed by cattle, then sheep, and finally goats.
A single sheep or goat is valid as a sacrifice on behalf of one person. However, a single camel or cow can be shared by up to seven people. This is based on the narration of Jabir (may Allah be pleased with him), who said: "In the year of Al-Hudaybiyah, we sacrificed along with the Messenger of Allah (peace and blessings be upon him) a camel on behalf of seven people, and a cow on behalf of seven people." (Narrated by Muslim)
(Note: The term "Badanah" used in the original Arabic text specifically refers to a camel in this context). And Allah the Almighty Knows Best.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.
Is it permissible for the guardian to give Sadaqa (voluntary charity) from the money of the orphans?
It is impermissible for the guardian to donate from the money of the orphans because he is entrusted with the safekeeping of that money, and is prohibited from donating it.
What is the due amount of food in expiation for perjury?
It is feeding ten indigent persons: 600 grams (for each) of the average food of your families such as rice, and it is permissible, according to Imam Ahmad Bin Hanbal, to give that amount in money if it was more useful to them.