How is it ensured that the rear-view mirror on the bike is working properly?

You selected both answer 1 (must be correctly adjusted) and answer 2 (may not be damaged), which is correct. According to German traffic regulations, a rear-view mirror on a bicycle must be in good working order. This means the mirror must not be damaged so you can see clearly, and it must be properly adjusted so you get a good view of the traffic behind you. These requirements ensure your safety and awareness while cycling. The rule about not extending beyond the handlebars is not a necessity for legality or proper function of the mirror. If you apply these principles, you'll know how to check if your bike's mirror is compliant in similar situations.