ANSWER:
1) The car is not accelerating, because for the the car to turn while accelerating down the street, it has to deaccelerate (reduce speed) due to CENTRIPETAL FORCE that is acting on the car during the turn. This force acts to bring the car in the direction where it has turned to.
2) You will feel the movement as everyone in the car will tend to fall to the left, while the car makes a right turn. This is because of CENTRIFUGAL FORCE, which is acting to take the car to a left direction, while the car is turning to the right direction.