When is a child instructed to fast?
A child is instructed to fast at the age of seven if they are capable of fasting and have reached the age of discernment, by analogy to prayer. They should be encouraged but not forced, so they can become accustomed to it. It is obligatory for their guardian, whether a father or another, to instruct them.
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.
When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?
It is offered after Tasleem.
Is it permissible to offer condolences to a non-Muslim?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to offer condolences (Ta'ziyah) to a non-Muslim upon the death of their relatives. This constitutes a form of benevolent treatment (Birr) that we have been commanded to observe. Allah Almighty states {what means}: "Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes—from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly." (Surah Al-Mumtahinah, 60:8). And Allah Almighty knows best.