So from the picture of the shunt it looks like the current you are measuring is the net current - amps out minus amps in. Fridge compressors are controlled via a thermostat and mains fridges, when running, typically consume about 65 watts. Fed from an inverter that would be about 5.5 - 7.0 amps at 12 volts, depending on the efficiency of the inverter. Of course the fridge will not be running all the time and the more efficient it is, the less it should run. It will consume near zero power when the compressor is not actually running.
If you are seeing the 1 amp out of the batteries when the compressor is running, and assuming there are no other devices consuming power, it would suggest that the solar panels are delivering 4.5 - 6.0 amps of the current required by the inverter/fridge and therefore the 1 amp on the meter is just the net drain on the batteries.
What's the device on the extreme right? It look like a fuse with a switch on it - going to nowhere!