What applies when you see this traffic sign?

Your answer is correct. This traffic sign indicates a built-up area ("Mehlem, Stadt Bonn"). In such areas, you can typically choose any lane suitable for your direction of travel, as indicated by option 1. Additionally, on multi-lane roads within built-up areas, vehicles in the right-hand lane are generally expected to move more quickly than those in the left-hand lane, which matches option 2.

However, the speed limit is not automatically higher than 50 km/h just because it is a multi-lane carriageway. Within built-up areas, the general speed limit is 50 km/h unless otherwise posted, so option 3 is incorrect in this context.

Remember, the key rule is that inside built-up areas, lane choice is flexible based on direction, and on roads with multiple lanes, slow vehicles should keep left while faster vehicles may pass on the right, but driving faster than 50 km/h requires explicit authorization through signs.