Was there any ice build up on the evaporator when you replaced the fan?
Don't forget to clear codes (in case you haven't)
I would expect a fan error to only come from an incorrect (out of desired range) speed signal, whilst this fault could be a board problem I would first remove and replace the connector on the main board for the fan signal in case there is any corrosion or bad connection (unlikely but possible).
It could also come from current sensing if the board has it and/or the temperature swings on the thermistor, (unlikely, but I don't know the program logic).
Another reason for large temp swings could come from a sticky refrigerant diverter valve, you can force the fridge to "Power Cool" mode which should open the valve fully. If possible monitor the air temp via external temp probe whilst doing any checks. Hopefully someone else can help you out further.