Complex situations
As mentioned already in other posts, declare dead on handover to ground personnel, not onboard, as local authorities may refuse to accept the body because of the confusing nature of the place of death. I know for a fact that if there is a birth onboard, the baby may be registered in the country that the aircraft belongs to, as it is considered (when the doors are closed) as the soil or land of the country in which it is registered. But when it comes to death, the logistics and state legalities of handling a body are complex - you almost have more rights when you are dead, as compared to when you are alive.
As for making a decision to divert, turn around, or continue with regards to medical emergencies: it is completely situational and would be in the best interests of the patient and at the call of the commander with due consideration (obviously) to safety of the flight first. Using onboard SATCOM communications with airline appointed doctors is the normal course of action, as well as use of onboard medical resources (medically trained passengers). It is a very difficult decision to make as the potential for big consequences exists in any decision taken. If no decision is taken, then time makes the decision for you.