Marsh
I see you are totally confused on the issue
#1 RV fridge on electric uses more power than a residential home 120v compressor fridge that is the same size
You don't run RV fridge of inverter...use the the propane , unless plugged in some where
#2 how much solar do you have , how many watts of solar on the roof
#3 a built in, inverter/converter combo will not create a loop, it does only one job at a time, it an either or thing
It charges if you have shore power or generator, it inverts when there is only battery power accessible
#4 a discharge loop can be created when a person adds a stand alone inverter ( as whole house) when that is a converter already installed,
in this 'install' you must have a way to turn off 120v to the converter, either by using the circuit breaker in the 120v section of your power panel, or by unplugging the converter from 120v
#5 no loop is created, if the stand alone inverter is wired to a dedicated circuit powering dedicated outlets for certain functions
Aka tv, or fridge or pc
And NOT wired whole RV, where it also powers the whole RV & converter