What is the ruling on a second congregation [being formed] in the mosque?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is disliked to deliberately seek to establish a second congregation in a mosque that is not one frequented by transient passersby — such as a neighborhood mosque with a regular, appointed imam — unless permission is granted by that imam, since doing so implies criticism and an affront to him. However, if the mosque is one frequented by transient passersby — such as mosques located in marketplaces — then a second or even third congregation is permissible there, whether or not it has a regular, appointed imam, and whether or not that imam gives his permission. This is because such mosques experience a continuous flow of people coming and going, so no implication of criticism toward the imam is perceived in the formation of multiple congregations in that setting. And Allah, the Exalted, knows best.
What is the ruling on performing Tarawih in sets of four rak‘ahs with only one Tasleem?
It is not permissible to combine more than two rak‘ahs with a single Tasleem in Tarawih prayer. Whoever does so, their prayer is invalid. Shaykh al-Islam Imam Muhammad al-Ramli (may Allah have mercy on him) stated: "If a person prays four rak‘ahs of the Tarawih prayer with a single Tasleem, it is not valid if they did so intentionally and with knowledge [of the prohibition]. Otherwise, it becomes an 'absolute voluntary prayer' (nafl mutlaq); because it is contrary to what has been prescribed." [Nihayat al-Muhtaj, Vol.2/P.127].
What is the virtue of Laylat al-Qadr?
It is enough to know its great status that Allah revealed an entire surah about it—Surah Al-Qadr. Moreover, the Quran was first revealed on this night.
Allah says {what means}:
"We have indeed revealed this (Message) in the Night of Power: And what will explain to thee what the night of power is? The Night of Power is better than a thousand months. Therein come down the angels and the Spirit by Allah's permission, on every errand: Peace!... This until the rise of morn!" [Al-Qadr/1-5]
The Prophet ﷺ taught us to observe I‘tikaf in the last ten nights of Ramadan, seeking Laylat al-Qadr. Whoever worships Allah and revives this night will receive the reward of worshiping for a thousand months—excluding Laylat al-Qadr itself.
What is the ruling on the ablution of one who cuts his nails, and is it permissible to cut them before the ritual bath for major impurity (janabah)?
Cutting nails does not invalidate ablution, and it is permissible to cut them before the ritual bath for major impurity. And Allah the Almighty knows best.