What is recommended for a Muslim to say on Laylat al-Qadr?
On Laylat al-Qadr, it is recommended for a Muslim to recite the supplication (du‘a) that the Prophet ﷺ taught Aisha (may Allah be pleased with her):
"O Allah, You are Most Forgiving, and You love forgiveness, so forgive me." [Narrated by Al-Tirmidhi]
Is it permissible to purchase the Udhiyah on installments?
It is permissible to purchase the sacrificial animal (uḍḥiyyah) on installments or by borrowing its price. However, it is not recommended for the poor to do so, because they are not required to offer a sacrifice, and Allah does not burden a soul beyond its capacity. If doing so would lead to negligence in providing for one's dependents (nafaqah wājibah), then giving precedence to obligatory maintenance over borrowing to buy the sacrifice is appropriate. This is based on the saying of the Prophet (peace and blessings be upon him): "It is sufficient sin for a person to withhold food from those whom he is responsible to support."
Furthermore, the sacrifice is valid from one who has a debt, but it is preferable (awlā) to repay the debt first, especially if the debt is due immediately (ḥāll). And Allah Almighty knows best.
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 swearing an oath by the Prophet ﷺ, and does such an oath take effect according to Imām Aḥmad ibn Ḥanbal, requiring expiation upon its breach?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Swearing an oath by a created being is disliked (makrūh) in our Shāfiʿī school. Shaykh al-Islām Imām al-Nawawī, may Allah have mercy upon him, states: "Swearing by a created being is disliked — such as swearing by the Prophet, the Kaʿbah, Jibrīl, the Companions, or the Prophet's family. Al-Shāfiʿī, may Allah have mercy upon him, said: 'I fear that swearing by other than Allah the Almighty may constitute an act of disobedience.' The scholars of the school explained this to mean: that is, something forbidden and sinful — indicating that he had some hesitation in the matter. Al-Imām stated: the established position of the school is that it is categorically not forbidden, but rather disliked. Furthermore, whoever swears by a created being, his oath does not take effect and no expiation (kaffārah) is required if he breaks it." [Rawḍat al-Ṭālibīn wa ʿUmdat al-Muftīn, Vol. 11/P.6]
According to the Ḥanbalī school, however, expiation becomes obligatory upon one who swears by our master the Prophet ﷺ and then breaks his oath. Imām al-Bahūtī al-Ḥanbalī, may Allah have mercy upon him, states: "No expiation is required for swearing by other than Allah the Almighty, even if the oath is broken — because expiation was made obligatory for swearing by Allah and His attributes, out of reverence for His names, and nothing else is equal to Him in this regard... except in the case of swearing by our Prophet Muḥammad ﷺ, for expiation becomes obligatory when one swears by him and then breaks the oath. This was explicitly stated in the narration of Abū Ṭālib, because he is one of the two conditions of the two testimonies of faith by which a disbeliever becomes a Muslim. Ibn ʿAqīl held the view that swearing by any of the other prophets, peace and blessings be upon them all, carries the same ruling." [Sharḥ Muntahā al-Irādāt, Vol. 3/P.441]. And Allah the Almighty knows best.