What is the ruling on performing ablution (wudu') and ritual bathing (ghusl) with Zamzam water?
It is permissible to perform ablution and ritual bathing with Zamzam water. However, scholars disliked using it for cleaning after relieving oneself (istinja'). And Allah the Almighty knows best.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.
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.