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.
Is it true that whatever is dry is pure even if there was impurity on it?
The impure material object does not soil (make impure) anything else unless the impurity is wet and transferable. But, if the impurity is dry or non-transferable, then there is no problem. Fuqaha has stated that: There is no disagreement between Muslim scholars that when a dry impurity touches something dry it does not make the latter impure.
I prayed while I was in the hospital after a bladder surgery, and my urine was connected to me and could not be disconnected that day. I prayed after performing tayammum with my finger because I was unable to stand. What is the ruling?
After Allah grants you complete healing, make up the prayers you performed with your finger to the best of your ability, at times that suit you. And Allah Knows Best.
What is the ruling on making a false oath?
Making false oath indulges its maker in Hell; therefore, he is obliged to repent, ask Allah for forgiveness and make an expiation; feeding 10 poor or providing clothes for them and in case of incapability of doing any of latters he should fast for 3 consecutive days. And Allah Knows Best.