Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?
The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.
What is the wisdom and purpose behind the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Among the wisdoms and purposes of the 'aqīqah are the following:
First: Expressing joy at the blessing of Allah the Almighty, rejoicing in the newborn, and giving thanks to Allah for this gift. Allah the Almighty says (what means): "If you are grateful, I will surely increase you." [Ibrāhīm/7]
Second: Proclaiming and publicising the lineage (nasab) of the child — and the 'aqīqah serves as an appropriate and fitting means to this end.
Third: Gladdening the hearts of family members, relatives, friends, and the poor by gathering them together over a shared meal. And Allah Almighty knows best.
What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.