YES. Codeine is addictive if you take codeine in large amounts or other than prescribed. This is even the case when codeine is prescribed by a doctor. We review what codeine is made of, and how you get addicted to codeine here.
Codeine only stays in your system for a couple of days. More about codeine detection windows for blood, hair, and urine tests here.
Yes. Codeine is a narcotic. In fact, codeine is both a medical and legal narcotic. Codeine is also a Schedule II controlled substance. More on codeine classification here.