During a flight from Amman to the UAE, while we were flying over Saudi Arabia, the captain announced that it was time to break our fast, coinciding with the exact time of sunset. After I had broken my fast with my first date, the captain apologized for the earlier announcement and clarified that the correct time would be in 20 minutes. Am I required to continue fasting on that day?
Whosoever break his fast at teh very first announcement to make up the missed day of Ramadan, since Allah, The Most Exalted, Said (What means): "then complete your fast Till the night appears" [Al-Baqara/187]. And Allah Knows Best.
Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
I used artificial nails on my wedding night, but I was surprised to find out that they require at least a week to remove. However, I performed all my prayers during that period. What is the ruling on those prayers?
If these nails prevent water from reaching one's skin then your prayer are invalid and obliged to redo all of them. And Allah Knows Best.
Should a minor fulfill his vow?
The vow of a minor is countless because he isn`t required to meet the Sharia rulings at such an age, and it is desirable for him to fulfill that vow once he reaches puberty.