General Rules

It is not permissible to perform autopsy on the body of a dead Muslim for the sake of education and other purposes.
It is only permissible, if the life of another Muslim depends on it—even if it is sometime in the future.

It is permissible to transplant an organ from an animal (including dogs and pigs) to a human being; the transplanted organ will be considered as an organ of the recipient; all rules will apply to it.
So salat will be permissible with it by considering it ritually pure (tahir) after it becomes part of the human body and its cells become rejuvenated.
(See the question-answer section below)

It is not permissible for a doctor to switch off the medical apparatus providing a Muslim patient with oxygen, even if he is brain dead, i.e. in vegetative state. This is because the human life in Islam is sacrosanct.
The doctor should not give in to the demand of the patient or his family-members for stopping medical aid.
If the doctor pulls out the plug and the Muslim patient dies because of it, he will be considered killer.

It is not permissible for a medical student to look at the private parts of anyone during his or her training for that profession, unless he would be repelling serious harm from a Muslim in the process—even if it is sometime in the future— .

It is not obligatory on a Muslim to investigate whether or not the medicine [given to him] consists of forbidden ingredients, even if the process of reading a result is easy for him.