Does friction always act opposite to the motion of the body? For context, please consider the following problem from an older AP Physics C: Mechanics practice exam:

Since the ball is rolling without slipping, there is static friction between it and the ground such that torque is exterted on it, making it rotate. If I understood correctly, the frictional force f, in this scenario, opposes the movement of the object, and it is zero if it stops rolling and starts slipping, or ceases contact with the surface. Therefore, at point A on the loop f would point downward, and in point B, since it is still rolling, it would point to the right like so:

However, the CollegeBoard answer sheet shows otherwise. It indicates that at point A f points upwards and at point B it does not act on the ball at all:

Does friction still act on the ball at point B? Is the friction on a rotating body opposite to its movement? If so, did CollegeBoard perhaps get the answer sheet wrong?
 A: Static friction on a rolling body does not always have to act "opposite to its movement". For example, take a sphere rolling up an incline. It's rotation is slowing down, so we know that static friction points up the incline, which is the direction the sphere is moving. Static friction opposes relative motion between the surfaces, not the motion of the center of mass of the sphere. The sphere surface "wants" to slide in the downward direction of the incline, so static friction points up the incline to oppose this.
And this simple example points us in the right direction in problems like these. For the incline as well as the problem you give, the only force that can change the rotational motion of the sphere about it's center of mass is the static friction force, as the other forces (weight and normal force) do not have a torque about the center of mass of the sphere. Additionally, since there is rolling without slipping, $v_\text{COM}=\omega r$. Therefore, how the speed of the sphere is changing can directly tell us about the static friction force. If the speed is increasing, then static friction has to act in the direction that increases the rotation of the sphere. If the speed is decreasing, then static friction has to act in the direction that decreases the rotation of the sphere.  If the speed is not changing, then there is no static friction force acting on the sphere.
This reasoning can be used to show that the solutions given to you for your specific problem are correct (think about how/if the speed of the sphere is changing at points A and B). There are no typos.
