Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
Is it permissible to pay the Zakah to my grandmother who lives alone in a rented accommodation with bad conditions noting she had three sons.
Zakah cannot be given to ascendants (parents and grandparents). It is obligatory for her sons and grandsons to provide for her, and they would be sinful if they fail to do so. And Allah Knows Best.
What is the ruling on the unification of Adhan?
All perfect praise be to AllahThe Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions. The unified Adhan is an act of Sunnah performed on behalf of a city's population. In addition, any Masjid that doesn’t have a Mua'than (The person who calls for prayers) and doesn`t raise the Adhan misses the reward of this great act. This is because Adhan should be raised for every group of people. However, the unified Adhan should be called in one Masjid and heard through all other Masjids. And Allah Knows Best.
Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?
The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.