Does Laylat al-Qadr move between the nights of Ramadan?
Laylat al-Qadr is definitely in Ramadan, and it is most likely in the last ten nights, especially on the odd-numbered nights.
For this reason, the Prophet ﷺ commanded observing worship in the last ten nights, and he himself used to dedicate those nights to worship. Many people put special effort into the 27th night of Ramadan, and they are rewarded in any case, whether they actually coincide with Laylat al-Qadr or not, because worshiping on any night of Ramadan carries great rewards.
What is the ruling on discharging one's zakāh obligation through the provision of a specific benefit (manfa‘ah) — such as performing a surgical operation for a patient, or providing housing to a tenant, and counting the value of this service as zakāh?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is obligatory to pay zakāh from the actual asset (‘ayn al-māl) upon which zakāh is due, except in the case of zakāh on trade goods ('urūḍ at-tijārah), which is paid based on their monetary value. In all cases, zakāh must be given in the form of tamlīk (a full transfer of ownership), based on the words of Allah, the Mighty and Majestic (which mean): "Zakāh expenditures are only for the poor and for the needy, and for those employed to collect [zakāh], and for bringing hearts together [for Islam], and for freeing captives [or slaves], and for those in debt, and for the cause of Allah, and for the [stranded] traveler — an obligation [imposed] by Allah. And Allah is Knowing and Wise" [at-Tawbah/60]. The letter "lām" (لِ) in this verse — as in "lil-fuqarā'" ("for the poor") — indicates possession/ownership (lām al-milk).
It is not permissible to fulfill one's zakāh obligation by providing a benefit or service (manfa‘ah) — such as housing, education, or medical treatment — in place of the zakāh itself. This is because zakāh must be paid as wealth (māl) that is transferred into the ownership of the poor recipient, whereas such services are intangible benefits that are not, in themselves, capable of being formally transferred in ownership (ghayr qābilah lit-tamlīk). And Allah, the Exalted, knows best.
What is the ruling on forgetting an integral of the prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Whoever forgets an integral (Rukn) of the prayer and remembers it before reaching the equivalent point in the subsequent unit (Rak'ah), must return to it (i.e., perform it) and complete his prayer, then perform the prostration of forgetfulness (Sujud al-Sahw) at the end of his prayer. However, if he remembers it after reaching the equivalent point in the subsequent unit, the Rak'ah in which the integral was forgotten is invalidated, and the current unit takes its place; he then completes a full Rak'ah to compensate and performs the prostration of forgetfulness.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.1/P.543): 'If he becomes certain at the end of his prayer, or after the Salam—provided the interval is not long according to custom and he has not stepped on an impurity—that he omitted a prostration from the final Rak'ah, he must perform it and repeat the Tashahhud, as his previous Tashahhud occurred before its proper place. If the omission was from a Rak'ah other than the final one, he must perform a full Rak'ah, because the deficient unit was completed by a prostration from the subsequent one, rendering the rest of that subsequent unit void.' And Allah the Exalted knows best.
Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?
It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.