To make the disc roll, a torque is required which requires tangential force on it. Here in this problem only friction can provide the tangential force.
(a) Frictional force at point B opposes velocity of point. Therefore, frictional force at the point of contact is in the direction as the arrow. Thedirection of frictional torque is such that it opposes the angular motion i.e. ω0. Since ω0 is normal to the plane of the paper in the inward direction, the direction of frictional torque is normal to paper and in outward direction.
(b) Frictional force at point B decreases the velocity of the point of contact B with the surface. The perfect rolling takes place when the velocity of the point B becomes zero. When this is so, the force of friction also becomes zero.