Acceleration has a direction, but its direction is notnecessarily necessarily the direction of motion. It is the rate at which the velocity is increasing/decreasing. The direction of motion is the direction of the velocity.
Why the car does not continue to accelerate backward while the brakes are applied
It does accelerate backward, but again, if it is accelerating backward it doesn't have to be moving backward. It is the resultant force that is acting in the backward direction, causing the decrease in velocity.