Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
What is the ruling on reciting the takbīr from Sūrat aḍ-Ḍuḥā to Sūrat an-Nās upon completing the recitation of the Qur'an (khatm)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is recommended to recite the takbīr from the beginning of Sūrat aḍ-Ḍuḥā through to the end of Sūrat an-Nās, and this is the recitation practice of the people of Makkah.
It is stated in Nihāyat az-Zayn (p. 65): "It is sunnah to begin each sūrah with the basmalah, since it constitutes a verse of it. It is also sunnah to say, before each sūrah — from aḍ-Ḍuḥā to the end of the Qur'an — 'Lā ilāha illallāh, wallāhu akbar' (There is no god but Allah, and Allah is the Greatest), based on what has been narrated regarding Imam ash-Shāfi‘ī (raḍiyallāhu ‘anh), who heard a man reciting this takbīr in prayer, and said to him: 'You have done well, and you have hit upon the sunnah.'"
And Allah, the Exalted, 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.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
