How about doctor's "If you don't go to a hospital and have a surgery, then you will die" -- is this a threat?

If the doctor would say: "I'm the only doctor who can help you with your problem and if you go to another doctor and ask him to operate you, you will die" he's likely outside of medical ethics.

But let's see we don't have a doctor but have a person who claims to be a witch. She goes around and diagnoses that people have a "dark curse" and unless the person pays them money to remove the curse the person will die. If that's someone's business model I don't think our courts would like kindly on that person.