Is it permissible for a woman who is observing `Iddah (waiting period) due to the death of her husband to travel for performing Umrah (Minor Hajj)?
A woman observing `Iddah of a revocable (Rajee`) divorce isn`t allowed to travel for Umrah except with the consent of her husband.
Is it permissible for the doctor to uncover the hair of a female patient out of necessity?
It is only permissible for him to do so when there is no female doctor, and he should examine the patient in the presence of one of her Mahrams (unmarriageable kin).
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 buying and storing gold bars for profit permissible or prohibited?
Buying and storing gold bars for profit is permissible, and there is no harm in it. And Allah The Almighty Knows Best.