Yes, in general those are the parts I assume your reference to compartment is a storage area near your residential frig that would house the inverter. Not sure where that compartment is located in reference to your Batteries.
Due to the high current drain on your batteries required by these Inverters, the Inverters are generally mounted near the batteries and then the AC output is run the longer distance to the actual frig, usually to a 110 VAC plug. There are many configurations of this circuit some automatically switching the residential frig from shore power when available to the Inverter when shore power not available. Your manual method of switching the plug would be the least complex regarding wiring.
This is a pretty common question so you may want to do a search on the forum say for residential frig or Inverter to get information on the operation as well as the various wiring configurations
Yes the manual will list current/power requirement of your frig
Added: These past posts will also list normal sizes of Inverters used to support these residential frigs
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