Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.
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 of Islamic Law on a father shaking hands with his son’s wife after she has been divorced three times?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The wife of one’s son is among the women permanently prohibited to the husband’s father as soon as the marriage contract is concluded, based on the saying of Allah the Exalted: “Prohibited to you are your mothers, your daughters, your sisters, your paternal aunts, your maternal aunts, your brother’s daughters, your sister’s daughters, your foster mothers, your foster sisters, your wives’ mothers, and your stepdaughters under your guardianship [born] of your wives with whom you have consummated marriage. But if you have not consummated marriage with them, there is no sin upon you. [Also prohibited are] the wives of your sons who are from your loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful.” [al-Nisāʾ/23]
This prohibition begins once the son’s marriage contract with his wife is complete, and it remains in force even if the son separates from her before consummation or before any seclusion (khalwah) with her. It is therefore permissible for the father to shake her hand and to be alone with her, provided there is no fitnah (temptation) and no suspicion.
It is stated in ʿUmdat al-Sālik (p. 204): “It is forbidden to marry… the wives of one’s fathers and of one’s sons. All of these women become prohibited by the mere contract, … all of that being a permanent prohibition.” End quote, with slight adaptation. And Allah Almighty knows best.
Can someone who begins a voluntary fast break it?
It is preferable for someone who begins an act of worship not to break it.
Allah the Exalted has said {what means}: "and let not your [good] deeds come to nought!" [Muhammad/33].
However, if a person starts a voluntary fast (nafl) and needs to break it, they are going against what is preferable, but there is no sin upon them.