Is washing both openings (Istinjaa`) a must before every ablution?
Washing the front and back openings (Istinjaa`) is a must in case they have an impurity, but if they do not, there is no need for that, and Istinjaa` is not a condition for the validity of ablution.
Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?
It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.
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.
Is it permissible for me to name my first son “Kassim” ?
The Prophet (PBUH) prohibited combining his name and his nickname, but using one of them is desirable.