A Force is required for any body to accelerate. As you said, the friction between the road and the tires of car cause it to move it in a circular path. But a force is also required to be acting on our body to make it move in that circle. And this force is provided by the friction between our body the seats. If this friction force is not enough to make our body move in circle with the car we would tend to fall outward, because we do not have enough force on our body to accelerate with the car. This is why we fall outwards in a turning car.
Also how do we know exactly that the force acts towards the centre and velocity is at right angles in circular motion?
This is true only if the body is moving in a uniform circular motion. The force could have components that are along and perpendicular to the direction of velocity of the body. The former, which is the tangential force would increase/decrease the speed of the body and the latter, which is called the centripetal force would cause it to move in a circle.
In case of uniform circular motion, the speed remains the same and so the force could not have any component in the direction of velocity because if it did speed would change. That's why it is perpendicular to velocity.