What is the ruling on offering an Udhiyah on behalf of another with their permission?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for a person to offer a sacrifice (Udhiyah) on behalf of someone else with their permission, even if the person performing it has not offered a sacrifice for themselves. It is stated in Sharh Manhaj al-Tullab (Vol.5/P.261) by Zakariya al-Ansari: "No one may offer a sacrifice on behalf of another without their permission... as opposed to when permission has been granted." And Allah the Almighty knows best.
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.
What is the ruling of Islamic Law on eating or drinking forgetfully while observing the kaffarah fasting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If someone eats or drinks out of forgetfulness while fasting, it is simply that Allah has fed them and given them drink. Their fast is not broken by this; rather, they should continue fasting. This ruling applies whether the fast is an obligatory one (like Ramadan), a make-up fast (Qada), an expiation (Kaffarah), or a voluntary (Nafal) fast. And Allah the Exalted knows best.
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.