What is the ruling on a person who broke the fast a day in Ramadan due to hardship?
He/she is obliged to make up that day.
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.
I am a woman, and my natural menstrual cycle lasts six days. In the evening, I perform the testimony (Tashahhud) for myself, and then I engage in sexual intercourse with my husband. After intercourse, I experience bleeding, either immediately or the next day. Is my intercourse with my husband during this time forbidden?
It seems that your menstrual cycle lasts seven days, not six. Therefore, you should wait until the bleeding stops, then perform ghusl and pray. And Allah Knows Best.
What should a person, who delayed making up missed fasts of last Ramadan due to the continuance of the same excuse, do?
It is permissible for one, whose excuse for not making up missed fasts of last Ramadhaan has continued, to delay fasting until the excuse ceases to exist, and he is considered neither sinful, nor obligated to pay a ransom. And Allah Knows Best.