What is incumbent upon the one offering the sacrifice if, after slaughtering the animal, they discover that one of its internal organs is damaged or diseased?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The presence of disease or defect in the internal organs of a sheep does not affect the validity of the sacrificial animal, unless the disease leads to the animal becoming emaciated and its meat becoming corrupted.
It is stated in al-Iqnā' (2/590) by Imam al-Shirbīnī: "The third disqualifying condition: an animal with a manifest illness — meaning one whose illness visibly results in emaciation and corruption of its meat. However, if the illness is minor and does not produce such effects, it doesn`t affect the validity of the sacrificed animal." And Allah Almighty knows best.
Is Zakah (obligatory charity) due on the items used in the trading process such as: cars , shops etc..?
No Zakah is due on equipments used in the trading process such as cars and the like.
If a person enters a mosque and finds the congregation in the final tashahhud, which is more virtuous — joining them or waiting for a second congregation to catch the opening takbīr (takbīrat al-iḥrām)?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If a worshipper finds a congregation that is about to finish its prayer, and he hopes to catch the entire prayer from the beginning with another congregation, it is more virtuous for him to pray with this first congregation and then repeat the prayer with the second one — provided he does not intend to confine himself to a single prayer. If, however, he intends to perform only one prayer, then it is more virtuous for him to wait for the second congregation rather than joining the first, so that he may attain the reward of congregational prayer for every single rakʿah.
Al-Khaṭīb al-Sharbīnī, may Allah have mercy upon him, states: "If members of a congregation enter the mosque while the imam is in the final tashahhud, al-Qāḍī Ḥusayn held that it is recommended for them to join him in prayer, and that they should not delay in order to form a second congregation. Al-Mutawallī, however, affirmed the opposite view, and al-Qāḍī's own statement elsewhere supports this latter position, which is the relied-upon view. In fact, it is more virtuous for a person who has missed part of the prayer with one congregation, and who hopes to catch another congregation with whom he can attain the entire prayer within its proper time, to delay so that he may catch it in full with them. This applies when he intends to confine himself to a single prayer; otherwise, it is more virtuous for him to pray with the first group and then repeat the prayer with the others." [Mughnī al-Muḥtāj,Vol. 3/P.186] And Allah the Almighty knows best.
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.