Can somebody help me in determine the direction of frictional forces at $A,B,C$?
This is my reasoning. If friction was not present due to the weight, the rod AB will fall down and hence the point A should move to the right. Hence $F_a$ is to the left. By resolution of horizontal force, $F_c$ is towards right. By taking moments at O for the sphere, $F_b$ should be downwards. These are wrong.
Frictional forces are always in the plane of contact. The frictional forces at A and C are horizontal while at B it is tangent to the sphere. Forces perpendicular to the plane of contact come from the rigidity of the elements in contact. As the ground under the sphere is considered to be rigid, whatever downward force, here from the weight of the sphere, is applied at C is resisted. That is independent of friction.
The rod wants to slip right at A. Because of the friction at A, the rod pivots about that point. There must be frictional force at A to the left to counteract the projected force of gravity. The rod wants to fall down, so makes a downward force at B. That is a frictional force which is counteracted by an upward force at B from the sphere. The sphere experiences a clockwise torque because of the force from the rod. That torque needs to be resisted at C, so the force on the sphere is to the right at C. The net horizontal force on the sphere plus rod needs to be zero, so the frictional force on the rod at A and sphere at C must be equal and opposite.