1) Why, despite this, doctor was in general respected and well-paid profession?

The faith-healing preacher, the witch-doctor, and the traditional healer are respected professions in the cultures where they occur. The Hippocratic physician was basically the traditional healer of Western civilization. He offered interventions that might kill, might cure, and were certainly impressive.

(It's worth noting that surgery was not within the traditional province of physicians. The original Hippocratic oath forbids physicians from doing surgery since they were not trained in it.)