A man has raped a woman and she gave birth to a baby boy. To whom should that baby be attributed?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
First of all, the adulterer must be punished according to the rules of Sharia and the baby isn`t attributed to him. Rather, it is attributed to the mother. This adulterer has committed a grave sin and incurred the wrath of Allah. We advise him to make sincere repentance to Allah and pray that Allah forgives him. And Allah The Almighty 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.
Is it permissible for a wife to leave her house without obtaining the permission of her husband, and not to come back unless he divorces her co-wife?
It is forbidden for the wife to leave without obtaining her husband`s permission, and it is impermissible for her to ask him to divorce her co-wife as this inflicts harm on the latter and such an act is forbidden in Islamic law.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.