Although it is not required that premed students have health-related work experience, it can certainly be helpful. Experiences of this kind indicate a sense of commitment to the practice of medicine. Volunteer and paid jobs can often be found in hospitals, nursing homes, or other settings. Such experience serves at least two purposes. It gives you a chance to see whether working with sick people is really what you want in a career and, at the same time, it provides a supervisor who can judge your ability to be successful in such a setting.
Prior experience is less available and less important for predent students.
In a number of states persons with drug-related convictions cannot be licensed to practice medicine. Medical schools are unlikely to admit persons who are known to violate these laws. Each medical school establishes its own admission requirements. The details of these vary considerably. If you are interested in a particular school, you should study its specific requirements.