Battery drain when not using..?

I have an Explorer 2000 which I use for camping/touring.

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I have a fridge that's permanently on - and use it also for kettle/toaster etc.

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I don't know a huge amount about how it works - but I saw someone comment about how it was more efficient to power from the DC rather than the AC. Before that I was running the fridge from the AC plug socket.

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Am I right in thinking the reason it's less efficient is because by using AC you are basically needing the machine to run an inverter/converter?

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I've noticed that if I forget to turn off the AC power after use the battery drains much quicker - even if nothing is plugged in.

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Is this right?

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