Is fasting obligatory for a child?
Fasting is not obligatory for a child until they reach puberty. Puberty is determined by well-known signs, the most common of which are: nocturnal emission (for both males and females), menstruation (for females), or reaching the age of fifteen lunar years.
A guardian must instruct their children to fast once they reach the age of discernment, which is around seven years old, if they are capable of fasting.
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.
How is the Night Prayer (Qiyam al-Layl) performed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Night Prayer (Qiyam al-Layl) refers to the voluntary (Nafl) prayers performed by a person after the Sunset prayer (Maghrib) and before the Dawn prayer (Fajr). As for Tahajjud, it is the voluntary prayer performed during the night specifically after waking up from sleep, as an act of devotion to Allah. Allah the Exalted says {what means}: "And from [part of] the night, pray with it [i.e., recitation] as additional worship for you." (Al-Isra/79). Thus, in terms of reward,Tahajjud is superior to voluntary prayers performed before sleeping. And Allah the Exalted knows best.
Which is superior: The Udhiyah (Sacrificial Offering) or giving its value in Charity (Sadaqah)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Performing the Udhiyah (sacrificial offering) is superior to giving its monetary value as charity (Sadaqah) to the poor and needy. This is because the Udhiyah is one of the manifest symbols of the religion. Allah the Almighty says {what means}: "That [is so]. And whoever honors the symbols of Allah - indeed, it is from the piety of hearts." [Al-Hajj/32]. This is further supported by the explicit and authentic Hadiths regarding its virtue, and the fact that the Prophet ﷺ and the Rightly Guided Caliphs after him consistently performed the sacrifice. And Allah the Exalted knows best.