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.
My father has debts and asked me to repay them years ago, and I promised him I would do so upon his death — is it permissible for me to go back on my promise given that I am unable to repay them, especially since he refuses to contribute to repayment on the grounds that the debt has become my responsibility by virtue of my promise?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
The established principle is that a father's debt is to be repaid from his own wealth, if he possesses sufficient means. As for the promise made by the son to repay it on his father's behalf, fulfilling such a promise is strongly recommended, and breaking it is considerably disliked. Shaykh al-Islām Imām al-Nawawī, may Allah have mercy upon him, states: "Fulfilling a promise is emphatically recommended, and breaking it is severely disliked. The evidences for this from the Qurʾān and the Sunnah are well known." [Rawḍat al-Ṭālibīn,Vol. 2/P.278] Shaykh al-Islām Imām Zakariyyā al-Anṣārī, may Allah have mercy upon him, further states: "The reason fulfilling a promise is not obligatory and breaking it is not forbidden is that a promise is in the nature of a gift, and a gift does not become binding except upon receipt." [Asnā al-Maṭālib fī Sharḥ Rawḍ al-Ṭālib,Vol. 2/P.487]
Given that the son does not possess the financial means to fulfil his promise to his father, breaking this promise falls beyond his capacity — and Allah does not burden a soul beyond what it can bear. Since the father himself possesses sufficient wealth to settle his own debt, repayment must be made from his own funds. Should he pass away before doing so, the debt is to be settled from his estate. And Allah the Almighty knows best.
What is the ruling on offering the sacrifice (uḍḥiyah) using the wealth of a minor or a legally incompetent person (safīh)?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
It is not permissible for the guardian (walī) of an orphan or a legally incompetent person (safīh) to offer the sacrifice (uḍḥiyah) on behalf of the minor or the safīh using their wealth, because the guardian is charged with exercising caution over their wealth and is prohibited from giving any of it away voluntarily, and the udḥiyah is a voluntary act of charity (tabarru'). The guardian may, however, offer the sacrifice using his own personal wealth. And Allah, the Most High, knows best.
What is the ruling on one who slept while firmly seated on the ground, regarding nullification of ablution?
The default ruling regarding sleep is that it nullifies ablution. An exception to this is one who slept while firmly seated on the ground; his ablution is not nullified by sleep if he wakes up while still firmly seated on the ground. And Allah the Almighty knows best.