Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.
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.
What is the ruling on eating from one`s Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Sacrifices (Udhiyah) are categorized into two types: the Vowed Sacrifice (Al-Mandhurah) and the Voluntary Sacrifice (Al-Tatawwu').
1. The Vowed Sacrifice (Al-Mandhurah)
The vowed sacrifice is obligatory due to the person’s specific oath. It is not permissible for the person offering the sacrifice, nor for those they are legally responsible for financially supporting (dependents), to consume any part of its meat or fat. Furthermore, it is not permissible to benefit from its hide, hair, or any other part.
If they do consume any part of it, they are required to give in charity an equivalent amount of meat or its market value [Tuhfat al-Muhtaj, by Ibn Hajar al-Haytami (9/364)].
2. The Voluntary Sacrifice (Al-Tatawwu’)
Regarding the voluntary sacrifice, it is permissible for the one offering it to eat from its meat, distribute it as gifts to the wealthy, and give it as charity to the poor.
The Obligatory Portion: It is mandatory to give at least a small portion of it in charity to the poor; this portion should not be less than approximately half a kilogram of raw meat. And Allah the Almighty knows best.
