What is the ruling on offering an Udhiyah on behalf of another with their permission?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for a person to offer a sacrifice (Udhiyah) on behalf of someone else with their permission, even if the person performing it has not offered a sacrifice for themselves. It is stated in Sharh Manhaj al-Tullab (Vol.5/P.261) by Zakariya al-Ansari: "No one may offer a sacrifice on behalf of another without their permission... as opposed to when permission has been granted." 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.
Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?
It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.
If the menses lasted for over than 9 to 10 days, considered menstruation?
If the duration of the bleeding does not exceed fifteen days, it is all considered menstruation, even if the usual pattern changes.