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.
What is the ruling on Tarawih prayer?
Tarawih prayer is a confirmed Sunnah (Sunnah Mu’akkadah).
What is the ruling on a mother giving the Zakat of her wealth to her children?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for a mother to give her children from the Zakat if they are among those who are eligible for it—such as being poor (Fuqara), possessing no wealth, and not being sufficiently provided for by the maintenance (Nafaqah) of others. This is based on the statement of the Messenger of Allah ﷺ regarding Zaynab, the wife of 'Abdullah ibn Mas'ud (may Allah be pleased with them both): (Your husband and your children are the most deserving of those upon whom you spend in charity) [Narrated by Al-Bukhari].
It is stated in [Al-Hawi al-Kabir, Vol. 8/P.537]: 'As for the wife, it is permissible for her to pay her Zakat to her husband from all the designated shares... Our evidence is the generality of the saying of Allah the Almighty: "Zakat expenditures are only for the poor and for the needy", and the Hadith of Abu Hurairah that the Prophet ﷺ said to Zaynab, the wife of 'Abdullah ibn Mas'ud: (Your husband and your children are the most deserving of those upon whom you spend), and this is taken in its general sense.' And Allah the Exalted knows best.
Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.