Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
How should I be kind to my atheist father?
Allah, The Exalted, has decreed and ordained his slaves to be kind with parents, even if they are polytheists, by honoring and obeying them in all that isn`t sinful, so that they might love Islam and embrace it as a result.
Ruling when Husband Utters Divorce Jokingly, or in the State of Intoxication or Anger
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The man who utters divorce while in the state of anger, his divorce doesn`t take place and the same ruling applies to the man who is forced to utter divorce because he is threatened to be killed or one of his organs cut off, in addition to other matters that scholars have mentioned in this regard. However, the man who utters divorce jokingly or while having intentionally drunk alcohol, his divorce takes place. And Allah The Almighty Knows Best.
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.