1. How is the patient? How is the patient progressing? How is the patient doing? and How is the patient coming along? These are various ways of asking about a patient’s recovery process, with no apparent previous information known. 2. How well is the patient coming along? This, to me, is no different in intent or usage. 3. Is the patient showing signs of improvement? Did the
Yes, that is correct. My answer may have been misunderstood. Your second sentence (#2.) has the same meaning as the first (#1.). Asking about the health of a patient is difficult, because the doctor cannot reveal confidential information; so a visitor merely asks for a general state of well-being.