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.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is it disliked to clip one`s nails at night, and to burn them afterwards?
It is recommended to bury hair and nails that have been removed and to conceal them in the ground. As for burning nails, we have not found any specific prohibition against it, but adhering to what is supported by evidence—burying the nails—is preferable. And Allah Knows Best.
Who is obligated to fast?
The one obligated to fast is the Muslim who is of sound mind, mature, capable of fasting, and free from obstacles such as menstruation or postpartum bleeding. And Allah Knows Best.