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).
Am I permitted to perform more than a prayer within single ablution?
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 of his family and companions.
You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified. And Allah 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.
Is it permissible to fish on Saturday?
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 of his family and companions.
It is permissible for Muslims to fish on any day, but the sons of Israel are the ones forbidden to fish on Saturday. Moreover, there is no evidence in Islamic Sharia prohibiting Muslims from fishing on that day. And Allah Knows Best.