What is the ruling on sacrificing a hornless sheep?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is valid to sacrifice a hornless sheep (al-Jamma’ or al-Jalha’). Similarly, a sheep with a broken horn is also acceptable; it does not affect the validity of the sacrifice even if the break causes bleeding, unless the injury is so severe that it leads to the spoilage of the meat. And Allah the Almighty knows best.
What is the ruling on forgiving a tenant next month's rent, with the intention of counting it toward zakāh al-māl?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It does not fulfill the obligation to count the rent owed on a house, or a portion of it, in lieu of zakāh. Rather, it is necessary to first transfer ownership of the zakāh amount to the poor person directly; only afterward may he be asked to pay the rent [from that money].
It is stated in ‘Umdat as-Sālik (p. 112): "If someone gives [money] to a poor person, stipulating that the recipient return it to him in payment of a debt owed to him, or says, 'I am making what you owe me into zakāh, so take it [as such]' — this is not valid. But if he gives it to him with the [unstated] intention that the recipient will use it to repay him, or says, 'Repay what you owe me, so that I may [then separately] give it to you as zakāh,' or the debtor himself says, 'Give it to me, so that I may [then] repay you with it' — this is valid, and there is no binding obligation for the recipient to actually fulfill this [informal understanding]."
We would also remind [the reader] of the ḥadīth of the Prophet ﷺ: "The Muslim is the brother of the Muslim: he does not wrong him, nor does he abandon him [to harm]. Whoever attends to the needs of his brother, Allah, the Mighty and Majestic, will attend to his needs. Whoever relieves a Muslim of a hardship, Allah, the Mighty and Majestic, will relieve him of one of the hardships of the Day of Resurrection. And whoever conceals [the faults of] a Muslim, Allah will conceal him on the Day of Resurrection." (Agreed upon). 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.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.