What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.
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.
Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
What should a person do if they suffer from an incurable illness that prevents them from fasting?
A person who has an illness that is not expected to be cured and prevents them from fasting must feed a needy person one mudd (600 grams) of food (such as wheat or rice) for each missed day instead of fasting.
Allah Almighty says {what means}: "and [in such cases] it is incumbent upon those who can afford it to make sacrifice by feeding a needy person." [Al-Baqarah/184].