Is it permissible to give my zakat to my grandson who is studying at university, while I am living abroad and my money is in my home country? Also, is it permissible to assign my father the responsibility of distributing the zakat to the people in my home country?
It is permissible to give zakat to a son whom his father is supporting if he is an adult and in good health, because his father is not obligated to support him, making him one of the poor among the Muslims. However, the student who may receive zakat is one who is diligent in seeking beneficial knowledge for the Muslims and is religious. Zakat should be paid in the country where the money is located, and appointing your father to distribute the zakat in the country where the money is is the correct approach. And Allah Knows Best.
Is vomit among the nullifiers of Wudu (ablution)?
Vomit does not nullify Wudu, but it is a Najaasah (impurity) that requires rinsing the mouth and washing whatever became dirty by it since the prayer becomes valid only after the removal of Najaasah. And Allah Knows Best.
Should one obey his mother even if she was wrong?
Obeying one`s mother is an obligation in matters that are beneficial to her and so long as she didn't drive her children to commit an act of sin.
A person is sponsoring an orphan and pays the sponsorship monthly. Is it permissible to pay this month's sponsorship from zakat money?
It is permissible to pay the orphan's sponsorship from zakat money if the orphan is poor and has no one to support them. The person must intend to count it as part of their zakat when paying the money. And Allah Knows Best.