so the device does save values like daily, monthly etc
Yes, it does. I am not sure, however, whether or not it keeps the accumulated values when it gets unplugged. Regarding the “power” value being 0W most of the time sounds a bit strange to me - well, for a fridge that may be normal behaviour though. To test the measurement unit, you can use a 60W light bulb, for example. This may be useful to check the calibration of the device and to check whether or not it indicates a constant power consumption.