What is the ruling of Islamic Law on wudu (ablution) when there is an adhesive substance on the hand that is difficult to remove?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The general principle is: if what is applied to the limbs of wudu' (ablution) does not form a barrier substance preventing water from reaching the skin, then the wudu' is valid despite its presence. However, if these substances prevent water from reaching the skin, the wudu' is not valid with their presence, and they must be removed so that water reaches the hair or skin without any barrier.
Shaykh al-Islam, the Imam an-Nawawi, may Allah have mercy on him, says: "If there is wax, dough, henna, or similar substances on some of his limbs [of wudu'], and this prevents water from reaching any part of the limb, then his purification (tahara) is not valid — regardless of whether the amount is much or little. But if there remains on the hand or elsewhere only the trace and color of the henna, without its substance [i.e., the physical residue itself], or the trace of a liquid oil such that the water touches the skin of the limb and flows over it, though it does not remain [as a barrier] — then his purification is valid." [Al-Majmu' , Vol.1/P.529]. And Allah, the Exalted, knows best.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
What is the ruling on sacrificing a castrated animal or one with a missing tail?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to sacrifice a castrated sheep; as it has been established that the Prophet (peace be upon him) sacrificed:
"...two large, fat, horned, white-and-black, castrated rams (Mawju'ayn—meaning having crushed testicles)." [Narrated by Ibn Majah in his Sunan].
It is not permissible to sacrifice an animal that is missing its tail, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, or udder; such an animal is valid for sacrifice. And Allah the Almighty 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.