A magnet is hung by a string and then' placed near a wire as shown. When the switch is closed, the magnet rotates such that the ends of the magnet move as indicated by the arrows. At the instant the switch is closed determine: the direction of the current through the wire segment nearest the magnet. Explain. the direction of the force exerted by the magnet on the wire segment (assume the magnet is in the position shown). Explain.

part 1: the current should be up, as the field of the magnet goes into a South pole so if I point the fingers of my right hand at the magnet, and have my thumb directed up, then my palm will be pointing left - the direction of the push. An upward current in the wire would correspond to what you called an anticlockwise current.

Part 2 : due to magnetic effects, the wire pushes on the magnet, so the magnet pushes on the wire. The magnet is free to move, so it does - and presumably in the direction of the force. So the magnet is being pushed to the right, meaning the wire must be pushed to the left. Of course if the wire is not free to move it won't move to the left, but it will still be pushed that way.