Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
Is it permissible for the heirs of the person who caused the accident (The Killer) to fast (The intended as an expiation for unintentional killing) on his behalf if the latter died in the crash?
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.
One who dies while liable for obligatory fast, his/her guardians have the choice to either fast on his/her behalf or feed one poor Muslim for each day of missed fast. This applies to Ramadan and other obligatory fast, and since expiatory fast is obligatory, feeding a poor person for each missed day or fasting on behalf of the deceased is obligatory as well. And Allah The Almighty Knows Best.
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 to move a grave from its current location to another place, for example, from a garden in a home to a cemetery, knowing that the grave has been there for a long time, about fifty years?
It is not permissible to move the deceased from his grave, as this may result in breaking his bones and violating his sanctity. Such actions are not allowed. And Allah Knows Best.