What is the ruling on mentioning Allah`s name upon slaughtering an animal?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is Sunnah for the slaughterer to say at the time of sacrificing the Udhiyah: (Bismillah - In the name of Allah); due to the saying of the Almighty: "So eat of that [meat] upon which the name of Allah has been mentioned" [Al-An'am/118]. It is not obligatory; if one leaves it out intentionally or forgetfully, the consumption of the meat remains permissible. And Allah the Almighty knows best.
Is it permissible to pay the Fitr Zakah (obligatory charity) of Ramadan on behalf of a dead person?
The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadan. And Allah Knows Best.
Who is the "Capable Person" for whom the Udhiyah is prescribed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The Capable Person (Al-Qadir): is the one who possesses wealth in excess of their own basic needs and the needs of their spouse, children, or anyone they are responsible for supporting, during the day of Eid and the three days of Tashreeq; as this period constitutes the designated time for the sacrifice. And Allah the Exalted knows best.
Is it permissible for household members to pool money for the Udhiyah and gift it to one of them?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for members of a household to pool their money together and gift the total amount to one individual among them so that he may offer the sacrifice (Udhiyah). In this case, the family members receive the reward for giving charity (Sadaqah), and the one performing the sacrifice includes them in the spiritual reward (Thawab).
Furthermore, slaughtering a single sheep (on one's own) is considered religously better than participating as one of seven people in the sacrifice of a cow or a camel. And Allah the Almighty knows best.