Problem is your battery. Since you are new you most likely have never used a multi-meter to read the voltage directly at the battery-terminals. All items mentioned run off battery.
Once the battery goes dead from insufficient charging, or a cell shorts out, the converter/charger may not be able to pass current through battery and circuit to power the 12v items even when plugged into shore-power.
Not all RV's are created equal. For now check voltage at battery and the battery-disconnect switch. If the battery voltage drops too low the switch may not function and batteries are disconnected from the 12v circuit.
A fully charged battery is 12.6+ volts (50% about 12.1 volts). If the voltage is in this range check the circuit-breaker for converter/charger to see if tripped. Also check for a burned out fuse for 12v output.