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).
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
Is it permissible to recite the Holy Qur'an or to play a recording at mourning gatherings? Or is it considered an innovation?
Whenever Qur'anic verses are recited, it is obligatory upon everyone to listen, otherwise; they should remain silent. And Allah Knows Best.
I`m a building contractor. I have been building a house for a client, but the construction process stopped for some reason. Unfortunately, currently, prices of materials have multiplied, is it allowed for me to demand an increase in the agreed price?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is more appropriate to approach the client and try to reach a mutually satisfactory solution. And Allah The Almighty Knows Best.