When is it Sunnah to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered on the seventh day from the birth of the newborn. According to the sounder position, the day of birth itself is counted as the first of the seven days. Thus, for example, if the child is born on a Saturday, the 'aqīqah is to be slaughtered on the following Friday. If the child is born at night, the count begins from the day that follows. And Allah Almighty knows best.
What are the valid excuses for abstaining from congregational prayer in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Concessions (Rukhsah) are granted to abstain from congregational prayer in the mosque due to general excuses, such as: rain that causes hardship in going out, strong winds at night, heavy mud that cannot be traversed without the risk of soiling oneself, hot winds, and extreme heat or cold. There are also specific individual excuses, such as: illness that makes walking as difficult as walking in the rain, severe drowsiness, evident hunger or thirst, the suppression of bodily wastes (urine, stool, or gas), and fear for one's life, limb, physical faculty, wealth, or honor, among other valid excuses. And Allah the Exalted knows best.
Which is better in night prayer: long standing (Qiyam) or long prostration (Sujood)?
Long standing (Qiyam) is better in prayer. However, a Muslim should also observe tranquility and composure in their prayer.
A man wishes to offer more than one uḍḥiyah (sacrificial offering), and intends by these sacrifices "on behalf of everyone whom Allah and His Messenger love." Is this intention valid?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The uḍḥiyah (sacrificial offering) is not valid with this intention, because if the sacrificial animal is from sheep or goats, it suffices for one person only; and if it is from cattle or camels, it suffices for seven persons.
However, one may sacrifice it on his own behalf, and then gift the equivalent of its reward to whomever he wishes.
Imam ar-Ramlī (raḥimahullāh) says: "Ash-Shāfi‘ī (raḍiyallāhu ‘anh) said: It is within the vastness of Allah's bounty, the Exalted, that He rewards the one giving charity as well. From this, the scholars of the madhhab said: it is recommended for a person to intend the charity on behalf of his parents, for example — for Allah, the Exalted, will reward them, without this diminishing his own reward in any way." He then relates, as the relied-upon position, the permissibility of saying: "O Allah, convey the reward of what I have recited specifically to so-and-so, and to the Muslims generally." Az-Zarkashī said: "For reward varies in degree — its highest form is what one designates specifically, and its lowest form is what one dedicates generally [alongside others]." [End of quote from Nihāyat al-Muḥtāj]. And Allah, the Exalted, knows best.