Is the blood money (Diyya) obligatory upon the anesthesiologist whose unintentional mistake led to the death of a patient, and who is responsible for it, and what should the doctor do concerning the patient's family?

If you undertook to treat a patient without sufficient expertise and caused his death, then you are liable for compensation due to your negligence. As for the other physician, he is not liable for compensation because he did not cause harm to the patient himself. You must seek absolution from the patient's guardians or pay them the blood money (diyah), which is incumbent upon your 'aqilah (male relatives on your father's side). There is no need to fear retribution (qisas) because you did not intentionally take his life.