Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. And Allah Knows Best.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
What is the ruling of Islamic Law regarding one who purchases a sacrificial animal (uḍḥiyah) and it then develops a defect before slaughter?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a defect that invalidates the sacrifice (uḍḥiyah) arises after its purchase — for example, if one purchased a sound, defect-free animal, and it then developed a limp, blindness in one eye, or a similar defect before slaughter — it does not fulfill the requirement of a valid uḍḥiyah, according to the Shāfi'ī school.
It is stated in Asnā al-Maṭālib fī Sharḥ Rawḍ al-Ṭālib (Vol.1/P.535): "Even if the limp develops [in the animal] while the knife is upon it, it still does not fulfill the requirement, because it is lame at the moment of slaughter — this is analogous to a case where a sheep's leg breaks and one hastens to slaughter it [in that condition]."
The Ḥanbalī school, however, held that if the one offering the sacrifice purchased the animal while it was sound and defect-free, and a defect then befell it afterward, the sacrifice remains valid and there is no obligation to replace it.
It is stated in Masā'il al-Imām Aḥmad, one of the Ḥanbalī reference works (Vol.8/P.4021): "I said: If a person purchases the sacrificial animal while it is sound, and it is then afflicted with illness, blindness in one eye, or a broken limb [before slaughter]? He [Imam Aḥmad] said: It is said that it still fulfills the requirement. Isḥāq said likewise, because he purchased it while sound, and the defect befell it only afterward, so it remains sufficient on his behalf." [End of quote]
Accordingly, a sheep afflicted with a defect that invalidates the sacrifice does not fulfill the requirement of a valid uḍḥiyah — whether the defect arose after purchase or during the slaughter itself — according to the Shāfi'ī school. However, there is no objection to following the Ḥanbalī position on this matter [as a valid alternative]. And Allah, the Most High, knows best.
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.