What is the ruling on mentioning Allah`s name upon slaughtering an animal?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is Sunnah for the slaughterer to say at the time of sacrificing the Udhiyah: (Bismillah - In the name of Allah); due to the saying of the Almighty: "So eat of that [meat] upon which the name of Allah has been mentioned" [Al-An'am/118]. It is not obligatory; if one leaves it out intentionally or forgetfully, the consumption of the meat remains permissible. And Allah the Almighty knows best.
Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?
Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. And Allah Knows Best.
What is the ruling on preparing food for someone who is not fasting in Ramadan?
It is forbidden to prepare food for someone who is breaking their fast without a valid excuse in Ramadan.
Doing so would be assisting in sin, and assisting in sin is itself a sin.
Allah says {what means}: "but help ye not one another in sin and rancour" [Al-Mai`dah/2]
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.