What is the right course of action here?

Your answer is fully correct. According to German traffic rules, at a pedestrian crossing, you must reduce your speed carefully and be prepared to stop (brake carefully) to ensure pedestrian safety. You also must allow pedestrians the right of way, especially the pedestrian on the right who is about to cross. This rule applies even if there are no visible road markings, because the pedestrian crossing signs indicate that this area is designated for pedestrian crossing. Continuing to drive without slowing down or stopping would be dangerous and against the rules. This is why options 1 (brake carefully) and 2 (allow the pedestrian to cross) are correct, and option 3 is incorrect.