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.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
I suffer from excessive gas, especially when I pray, and I redo my ablution more than seven times. I have obsessive thoughts about this matter, even though I went to a doctor and was given medication that did not help. What should I do?
If the release of gas stops at certain times between prayers, you should wait for that time, perform ablution, and pray. However, if it is continuous, you should perform ablution after the prayer time begins and pray, and the release of gas during the prayer is excused. And Allah The Almighty Knows Best.
Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?
It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.