What is the expiation for perjury?
Perjury is forbidden and one of the major sins that require turning to Allah in repentance, seeking His forgiveness, giving back rights to whom they belong, or seeking their forgiveness, and expiating for that oath.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah 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, rump, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, rump, or udder; such an animal is valid for sacrifice. And Allah the Almighty knows best.
Is a person rewarded for refraining from all that breaks their fast when required to do so, and is it considered a valid fast?
If a person eats or drinks thinking that Fajr has not yet arrived, but then someone informs them that Fajr had already begun, they must refrain from eating for the rest of the day and make up the fast later.
If they observe the required restraint (imsak), they will be rewarded for obeying the command because fulfilling an obligation brings reward.
However, this is not considered a valid fast in terms of rulings. For example:
● It is not disliked (makruh) for them to use a miswak after noon.
● They are not encouraged to hasten the breaking of the fast at sunset.
● Other fasting-related rulings do not apply to them.