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.

Is it permissible for a woman who broke fasting due to a delivery to pay a ransom?

She should make up for the missed fasting days once she becomes ritually pure, but it is impermissible for her to pay a ransom while being able to fast.

I am a disabled woman who has vaginal discharges and can`t control her urine. Therefore, I combine prayers. Is that permissible?

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 his family and companions.

According to the Hanbali doctrine, it is permissible for the sick to combine prayers. In your case (Asker), it is better that you delay the noon prayer until a few minutes before the afternoon prayer in order to minimize the time span between the two and perform each alone. In addition, you can do the same with sunset and evening prayers. Finally, we ask Allah to bless you with recovery. And Allah Knows Best.

I want to buy a house by having a loan from a bank?

If taking a loan from usrious banks it is impermissible; on the other hand, if this took place through Islamic ones then it is permissible to get the loan, since Allah the Most Exalted Said (What means): "And Allah has made buying lawful and forbidden usury (riba)." And Allah Knows Best.