Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
Is keeping money in and taking profits from the Islamic Bank lawful?
If Allah Wills this is lawful, because they stipulate on theselves to work in accordance to the guidlines of Islamic Law. And Alalh Knows Best.
A woman used contraceptive pills, and her menses exceeded (15) days, is it permissible for her to fast?
The maximum of menstrual blood is (15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah (bleeding outside the monthly period), and in this case she should perform Ghusl (ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses. And Allah Knows Best.
The supplication: "O Allah, we do not ask You to avert the decree, but we ask You for kindness in it." Is this Supplication Halal or Haram?
We are obliged to supplicate Allah, so when supplicating we comply with Allah's Ordainments, and making supplications that are reported in the authentic texts is better. And Allah Knows Best.