What can be the consequences if the tow-bar of a towing coupling has longitudinal play?

You answered correctly. Longitudinal play in the tow-bar means that there is unwanted movement along the length of the coupling, which should be securely fixed. This extra movement causes repeated stresses and vibrations at the attachment points, making it possible for cracks to develop in the cross member where the towing coupling is mounted (answer 1). Over time, this can also lead to the towing coupling itself tearing off (answer 2), which is a serious safety hazard. However, it does not specifically cause overload on the shock absorbers of the rear axle, so answer 3 was not correct. Understanding how improper attachment or wear in towing components can lead to structural failures and dangerous situations is important for vehicle safety.