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 for my brother, whom I had suckled, to conclude a marriage contract between his daughter and my son?
Such marriage is impermissible since one`s nephew in this situation is considered an uncle to one`s daughter; consequently, he is the brother of her father by suckling. In such cases, the people in question should go to court to prove the suckling.
Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?
If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.
After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.