Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
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).
What is the ruling on performing voluntary prayers during official working hours?
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
There is no harm if there was break time during official working hours, but if not then it is impermissible. And Allah Knows Best.
Is permissible to include a will requesting that a Holy Qur'an buried along with me?
It is not permissible to include a will requesting that a Quran be buried with the deceased in their grave. This is because the body of the deceased typically decomposes and may release impure substances, and it is not allowed to expose the Quran to impurity. Intentionally desecrating the Quran is an act of disbelief. Instead, read the Quran during your lifetime, as it will benefit you after death. And Allah Knows Best.