In case of (theft) damage, should I go ahead and repair or do I need permission from the insurer?

Act like ‘a good family man’ and make sure the damage does not worsen both materially and in terms of production loss. You do not need permission to repair but make sure that the damage can be assessed by an expert afterward: take photos and keep damaged material until the insurer or expert says it can be removed. Starting restoration on time, however, does not mean that all damage is actually insured. This has to be determined afterward by the insurer.