When is it Sunnah to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered on the seventh day from the birth of the newborn. According to the sounder position, the day of birth itself is counted as the first of the seven days. Thus, for example, if the child is born on a Saturday, the 'aqīqah is to be slaughtered on the following Friday. If the child is born at night, the count begins from the day that follows. And Allah Almighty knows best.
What is the ruling on swearing an oath by the Prophet ﷺ, and does such an oath take effect according to Imām Aḥmad ibn Ḥanbal, requiring expiation upon its breach?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Swearing an oath by a created being is disliked (makrūh) in our Shāfiʿī school. Shaykh al-Islām Imām al-Nawawī, may Allah have mercy upon him, states: "Swearing by a created being is disliked — such as swearing by the Prophet, the Kaʿbah, Jibrīl, the Companions, or the Prophet's family. Al-Shāfiʿī, may Allah have mercy upon him, said: 'I fear that swearing by other than Allah the Almighty may constitute an act of disobedience.' The scholars of the school explained this to mean: that is, something forbidden and sinful — indicating that he had some hesitation in the matter. Al-Imām stated: the established position of the school is that it is categorically not forbidden, but rather disliked. Furthermore, whoever swears by a created being, his oath does not take effect and no expiation (kaffārah) is required if he breaks it." [Rawḍat al-Ṭālibīn wa ʿUmdat al-Muftīn, Vol. 11/P.6]
According to the Ḥanbalī school, however, expiation becomes obligatory upon one who swears by our master the Prophet ﷺ and then breaks his oath. Imām al-Bahūtī al-Ḥanbalī, may Allah have mercy upon him, states: "No expiation is required for swearing by other than Allah the Almighty, even if the oath is broken — because expiation was made obligatory for swearing by Allah and His attributes, out of reverence for His names, and nothing else is equal to Him in this regard... except in the case of swearing by our Prophet Muḥammad ﷺ, for expiation becomes obligatory when one swears by him and then breaks the oath. This was explicitly stated in the narration of Abū Ṭālib, because he is one of the two conditions of the two testimonies of faith by which a disbeliever becomes a Muslim. Ibn ʿAqīl held the view that swearing by any of the other prophets, peace and blessings be upon them all, carries the same ruling." [Sharḥ Muntahā al-Irādāt, Vol. 3/P.441]. And Allah the Almighty knows best.
What is the ruling on sacrificing a castrated animal or one with a missing tail?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to sacrifice a castrated sheep; as it has been established that the Prophet (peace be upon him) sacrificed:
"...two large, fat, horned, white-and-black, castrated rams (Mawju'ayn—meaning having crushed testicles)." [Narrated by Ibn Majah in his Sunan].
It is not permissible to sacrifice an animal that is missing its tail, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, or udder; such an animal is valid for sacrifice. And Allah the Almighty knows best.
What is the ruling on wiping the head during ablution from behind a barrier like a headscarf (hijab)?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. As for one who has a turban or headscarf on their head, it is permissible for them to wipe over it after wiping a part of their head in any place. This is easily done at the front of the head. This means the woman begins by wiping the front of her head from under the headscarf, then completes the wiping to the back of the head from over the headscarf. If the woman wipes over the headscarf on her head and the moisture reaches the scalp or some hair within the boundaries of the head, it suffices for wiping the head. And Allah the Almighty knows best.