For the ME Inverter/charger you most likely have a remote panel like the one below.
I have circled the two most important buttons on the control. One turns on the charger and one turns on the inverter. The charger will only work when the Van is plugged into Shore Power, best practice is have the charger off, plug-in and then turn the charger on. The corresponding LED will light up if the charger is on. While the charger is on the display will most likely be in Bulk, Absorption or Float charging. Float will mean the battery has been fully charged.
The inverter button will work when either plugged in to shore power or not. But, it will be in two different states. If plugged in and the inverter is on you will be suppling AC from shore power, if that was to fail, the inverter will automatically come on and supply AC.
If you are not plugged in, then you will not have any AC (120 Volt) power unless you turn the inverter on, and depending on the settings will need to see some minimal load. For best battery life practice it is best to leave the inverter off, until you need to use something that is powered off of 120 volts. When done, turn the inverter off. You can leave it on buy being on standby will use up power on it's own.
I would think that the ACR would be installed inside, I haven't seen tany "Sportmobiles" with it installed outside from factory. The most likely installed device will be the Blue Sea 7620.
The method 86Scotty described would be a good way to check if it is working, in fact I generally would recommend two of those plug in meters one for a Ford outlet and one for a Sportsmobile outlet. The ACR also makes a very noticeable clunk when connecting and disconnecting.
When you start the van the alternator should bring the charge voltage up into 14.x voltage range. The ACR will close when the voltage is above 13.0 volts for 90 seconds or 13.5 volts for 30 seconds. If the ACR closes the voltage on Sportsmobile 12 volt outlet will be close to the voltage of the van 12 volt outlet. They will not be the same because of some voltage loss, but should track. It is possible that the ACR also has the control wire connected to the Van "run" circuit, which means it will close as soon as the van is running.
Turn the van off and the voltage will drop and once it 12.75 for 30 seconds or 12.35 for 10 seconds it will disconnect.
When plugged into shore power and charging with your magnum, it will work pretty much the same way, except it be based off of the charge voltage on the Magnum.
I made a video on the operation of the unit a while back, it can be found here Understanding the Blue Sea 7620 or 7622