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.
What is the ruling on having a second congregational prayer in the mosque?
All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions It is disliked to have a second congregational prayer in the mosque which isn`t visited by travelers like the neighborhood`s mosque, and which has an appointed Imam, save with the latter`s permission. Nevertheless, if the mosque is visited by travelers, it is permissible to have a second and a third congregational prayer, whether it has an appointed Imam or not, or whether he permits that or not. And Allah Knows Best.
Should a pregnant woman who broke fast because of pregnancy make it up, and is a ransom due on her?
The pregnant and the suckling, if they fear for their health, may break their fast and make up for it, and no ransom is due on them. However, if they broke fast in fear for the fetus and the baby, then they are obliged to make up for it, and pay the ransom which is feeding a needy person for each of the missed fasting days. 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.