The easy way to determine which 120V sockets are supplied by the inverter is to disconnect the shore power and turn on the inverter, then take a A/C volt meter and test the voltage at all sockets. If you do not have a meter, you can use a lamp or something that will light up when 120V A/C is present.
As for as the current draw is concerned for the new refrigerator, I would not be concerned because the new residential style units for RV use have a very low current draw and any existing inverter circuits should supply enough current.
Gerald