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.
What is the ruling on performing Umrah after the latest expansion of the Mas`aa (the passage between As-Safa and Al-Marwah), is it permissible, or not?
Yes, it is permissible to perform Umrah after the latest expansion of the Sa`y area since making Sa`y between As-Safa and Al- Marwah is already observed. And Allah Knows Best.
What is the ruling on visiting a deceased's grave and supplicating Allah for him by his wife? Is the reward of reciting verses of the Holy Qur'an reaches the deceased?
There is no harm on visiting graveyard by woman with the intention of piety so long as they are dressed in accordance to the Islamic teachings. We ask Allah, The Almighty that the reward of reciting the Holy Qur'an on dedicated to the deceased reaches him. And Allah 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.