In daylight hours, when riding a motorcycle, the low beam must be on in any case, whatever the visibility or other conditions.
Clause 133 of the rules lists the cases in which, during daylight hours, a vehicle must have its low-beam headlights on to make itself visible. The first line of the list is motorcycles and mopeds, with no further condition. So when riding a motorcycle, the low beam must be on in any case. Note: the list does not cover all vehicles — an ordinary passenger car is not subject to this requirement.
Option 1. In low visibility, lights are required for everyone, but on a motorcycle they must be on in the daytime too, whatever the visibility.
Option 2. For a motorcycle, the daytime lights requirement applies in all cases, not only when moving a faulty motorcycle.
Option 4. Transporting a sick passenger has nothing to do with the rules for switching on the low-beam headlights.