The national electrical code will allow it. however it is not common practice because refrigerator compressors will often times trip them causing food spoilage.
GFI's work the same as any other outlet except that the will trip when a short is detected. So it should be fine. Just make sure the plug is the same voltage as what the fridge requires.
yes,and you should. all a gfci outlet does is protects the rest of the electrical system (and more importantly,you) if the device attached to the outlet malfunctions/short circuits.
