A little rust on the brake pad backing plate isn’t unusual. I doubt that is the cause. The forces which cause the brake pedal to return to its nominal position after you press it down are a combination of
- Springs in the master cylinder
- Hydraulic fluid forces equilibrating in the caliper piston
- Sometimes there is a return spring on the brake pedal too
Your mechanic will just have to go through those one by one. The first thing to check is that the master cylinder fluid is clean and at the correct range. Beyond that, most likely causes would be a spring broken in the MC, one of the MC pistons is sticking, a caliper piston is sticking, a flexible brake hose is collapsing, or something’s wrong with the ABS.
It’s important you get this looked at asap. From what you say, there’s definitely something wrong w/your brakes. When a car doesn’t stop correctly, that’s something that can be very dangerous.