About Required lighting and the MOT (APK): which statement is WRONG?
The passenger-car requirements name no fire extinguisher and no first-aid kit.
In fog you switch to full beam, because that gives more visibility.
'If visibility is less than 50 metres due to very dense fog or heavy snowfall (NOT in rain!) you may switch on your rear fog light.' In rain the rear fog light stays off, even below 50 m visibility.
Besides the owner/keeper, the driver is ALSO liable, as soon as the motor vehicle is actually driven on the road.
Explanation
trap: more-light-is-better reflex. By day with seriously impaired visibility (such as fog) dipped headlights are required, not full beam. Full beam is moreover forbidden when meeting or following other traffic