What are the conditions that must be met for the 'aqīqah to be valid?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is like the recommended uḍḥiyyah in terms of the type of animal, its age, and its required characteristics — since it is a recommended slaughter and therefore resembles the uḍḥiyyah in its rulings.
It is agreed upon without any difference of opinion that the 'aqīqah is not valid with any animal other than livestock (al-na'am — camels, cattle, and sheep). Likewise, an animal with a disqualifying defect — such as obvious illness, lameness, or blindness in one eye — does not suffice, as has previously been explained in the rulings of the uḍḥiyyah. And Allah Almighty knows best.
What is the ruling of Islamic Law on sitting between the two prostrations, and what is the ruling on the dhikr recited during it?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
Sitting between the two prostrations (al-jalsah bayna al-sajdatayn) is one of the pillars (arkān) of the prayer, while the dhikr recited during it is Sunnah according to the Shāfi'ī scholars. It is recommended (mustahabb) to say what was narrated from Ibn 'Abbās (may Allah be pleased with him), who said: "The Messenger of Allah (peace and blessings be upon him) used to say between the two prostrations in the night prayer: 'Rabbi ighfir lī, warhamnī, wajburnī, warzuqnī, warfa'nī' (My Lord, forgive me, have mercy on me, make good my deficiencies, provide for me, and raise me)." If one were to say a different supplication instead, such as "Rabbi ighfir lī" (My Lord, forgive me), the prayer would still be valid.
If the worshipper omits this dhikr between the two prostrations, whether intentionally or out of forgetfulness, their prayer remains valid and nothing is required of them, though they miss the reward of following the Sunnah. Leaving it out does not necessitate the prostration of forgetfulness (sujūd al-sahw).
It is stated in Hāshiyat al-Bājūrī 'alā Sharḥ Ibn Qāsim 'alā Matn Abī Shujā' (Vol.1/P.298): "The eleventh — i.e., of the eighteen pillars — his statement: 'sitting between the two prostrations,' meaning even in a supererogatory (nafl) prayer... his statement: 'with the supplication that has been narrated concerning it,' meaning: 'Rabbi ighfir lī, warhamnī, wajburnī, warfa'nī, warzuqnī, wahdinī, wa 'āfinī' (My Lord, forgive me, have mercy on me, make good my deficiencies, raise me, provide for me, guide me, and grant me well-being). Al-Ghazālī added: 'wa'fu 'annī' (and pardon me). Al-Mutawallī also added: 'Rabbi hab lī qalban taqiyyan, naqiyyan min al-shirk, bariyyan lā kāfiran wa lā shaqiyyan' (My Lord, grant me a heart that is God-fearing, pure from associating partners with You, innocent, neither disbelieving nor wretched)."And Allah, the Most High, knows best.
Does buying meat equivalent to the weight of a slaughtered animal and distributing it avail for an udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
That does not avail for the sacrifice (uḍḥiyyah), because the sacrifice necessarily requires slaughtering an animal from the category of anʿām (camels, cattle, and sheep/goats) within a specified time.
Rather, that is considered a form of charity (ṣadaqah) for which one is rewarded, but not an udhiyah. And Allah Almighty knows best.
What is the ruling on a person in a state of major impurity (junub) or a menstruating woman (ha'id) reciting the Quran from memory?
It is not permissible for a menstruating woman, a postpartum woman, or a person in a state of major impurity to recite anything from the Quran, whether from memory, from the Quran, from a phone, or a computer. It is also not permissible for them to touch the Quran, based on what was reported from Ali bin Abi Talib that the Prophet (peace be upon him) was not prevented from anything regarding the Quran except major impurity (janabah). (Reported by al-Tirmidhi who said it is a hasan sahih hadith). Menstruation and postpartum bleeding are analogous to major impurity (janabah) as they are all major impurities (hadath akbar).
For those mentioned, it is permissible to mention Allah and supplicate even with verses from the Quran, provided they do not intend them as recitation of the Quran, but intend them as remembrance (dhikr) or supplication (du'a). And Allah the Almighty knows best.