I may be worrying unduly, but I pulled the fridge out to clean the floor and around the fridge etc. I noticed that the the copper piping on the back of the fridge has gone black in areas and sort of verdigris spots. Is that normal?

Copper goes that colour when exposed to moisture.

Likely nothing more than water from the atmosphere condensing on the cool copper coils. - I wouldn't be unduly worried.

Well done you! I have only moved my fridge once since I bought it. That was when we 'lost' our new Kitten who was hiding behind the motor in the back.