What is the ruling on mentioning Allah`s name upon slaughtering an animal?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is a Sunnah (prophetic tradition) for the person slaughtering to say: "Bismillah" (In the Name of Allah), though the most complete and perfect phrasing is to say: "Bismillah ar-Rahman ar-Rahim" (In the Name of Allah, the Most Gracious, the Most Merciful). This is in accordance with the words of Allah Almighty: "So eat of that [meat] upon which the name of Allah has been mentioned." (Al-An'am/118)
However, pronouncing it is not an obligatory requirement (Wajib). If someone omits it—whether deliberately or out of forgetfulness—the meat remains entirely lawful (Halal) to eat, though purposely omitting it is considered disliked (Makruh). And Allah the Almighty Knows Best.
Can Zakah or Zakat al-Fitr be given to a poor brother?
Yes, it is allowed to give Zakah or Zakat al-Fitr to a poor brother, as he is considered among the eligible recipients.
Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (Makruh) for a person in a state of minor ritual impurity (Hadath Asghar) to perform the Adhan. However, if he does so, his Adhan is considered valid and fulfills the sunnah of the Adhan despite it being disliked. And Allah the Exalted knows best.
What is the monetary value for the expiation of an oath (Kaffarat al-Yamin)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The expiation for an oath (Kaffarat al-Yamin) consists of feeding ten (10) needy persons. This is estimated at 600 grams of rice per person. It is also permissible to pay its value in cash, which is estimated at one dinar (per person). And Allah the Exalted knows best.