Examples of major hospitals would be institutions like Massachusetts General Hospital, or National University Hosptial in Signapore. This isn't meant to be too restrictive, you could also read this as affecting more than ten thousand concurrent patients. The intent is that it is both legal somewhere and has gained some amount of public acceptance.

Advertise means anything comparable to how hospitals currently treat the services they provide, for instance, Mass General currently advertises cancer treatment.

Primary method of diagnosis means that an AI evaluates symptoms and delivers a diagnosis which is expected to be followed in most cases. The diagnosis may be checked by a physician, but a physician is not using the AI as a tool. A symptom of this might be a significantly lower doctor to patient ratio than is currently common. The recent Alzheimer research, for example, would be a supplementary method of diagnosis.