Does a Quran broadcaster sin if he shift to another surah or chapter without informing the listener?
The Quran must be broadcast as it was recited by the reciter and in a manner that conveys respect and reverence. And Allah The Almighty Knows Best.
Is it permissible for a woman who broke fasting due to a delivery to pay a ransom?
She should make up for the missed fasting days once she becomes ritually pure, but it is impermissible for her to pay a ransom while being able to fast.
What is the authenticity of the supplication: "O Allah, bring it upon us with blessings and faith, safety and Islam, and success in what You love and are pleased with. My Lord and your Lord is Allah"?
On the authority of Talhah Ibn Ubayd Allah (may Allah be pleased with him) who reported that the Prophet (PBUH) would say when he saw the crescent moon: "O Allah, let this moon appear over us with blessings and faith, safety and Islam. My Lord and your Lord is Allah."
This was narrated by Tirmidhi (Hadith no. 3451), who said: "It is a Hasan (good) Hadith."
And Allah The Almighty Knows Best.
Is It Permissible to Divorce One's Wife for not Praying
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
You should do your best to save her from hellfire by making her observe daily prayers on their prescribed times, even if this means giving her a generous incentive. However, if she insisted on her position, then it is permissible for you to divorce her. And Allah The Almighty Knows Best.