How often does the refrigeration cycle repeat itself? I have read that the compressor runs at about 1000 rpm. Does that mean that the frequency of the cycle is 1000/60=17 Hz?
No, that just means that the compressor delivers a given amount of refrigerant 1000 times a minute assuming a simple piston type compressor.
If you know the mass of refrigerant and the thermodynamic cycle, you can find the amount of heat transferred as all the refrigerant goes around one cycle.
Compare that with rate of cooling the device produces, and you know how long each cycle takes.