the most common thing to happen on the rear drums is Heat will warp the rear drums, causing a vibration while stopping. If you have your E-Brake set for a few days it can cause the shoes to stick when released (The bang type feeling when you moved).
Most likely your drums are out-of-round ; or not completely Circle anymore.
Its ok to drive the car on bad brakes. The only thing you want to be weary of is over-extending the rear brake cylinders if the shoes are too thin. If the shoes are dangerously thin, it can cause the brake cylinder to push out farther than its supposed to, and you will loose your brake fluid and loose control of your brakes (needing to use the emergency brake to stop).
If your mechanic recommended replacing the rear drums ; I would suggest replacing the rear drums / shoes / spring kit all together as soon as possible.
The surface rust on the outside of the drum will not cause braking problems, its rust on the inside where the shoes and drums contact.