Where should a woman following her husband or another man in prayer stand?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If a single woman prays with a man—whether she is his wife or a non-mahram (Ajnabiyyah)—the Sunnah is for her to stand behind the Imam and be shielded by him. If the Imam is leading both a man and a woman, the man should stand to the Imam's right, and the woman should stand behind the male follower (Muqtadi). In this way, she is shielded from the Imam by the male follower and remains at a distance from the follower and his line of sight. And Allah the Exalted 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.
Is it a condition that one should offer two sacrifices for a male newborn?
It is desirable to offer two sheep for a male newborn, and one for a female newborn. Offering one sheep for the male newborn is also permissible as it observes the Prophet`s Sunnah in this regard.
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.