I'm not sure what you mean by 'reducer'. I'm thinking you mean an adapter to convert the round receptacle to a flat 4 pin plug. Which shouldn't cause any problem.
There are fuses behind the passenger side kick panel as well. Have you checked all those? Also the relays. The only thing that I can think of at this point that would be in common with the elements that are malfunctioning is the Body Control Module. The BCM controls your fogs and the headlight functions when in Auto. However, if a relay feeding the BCM has gone bad, you could experience similar symptoms.