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 to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
Is Zakah (obligatory charity) obligatory on indebted merchant?
Debt doesn`t abrogate the dueness of Zakah, thus a debtor who has money, articles of merchandise, or other Zakah funds at his disposal should pay their Zakah.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.