On my 2010, if the inverter is on, the TV and the DVD player are in the stand by mode, the red lights are on, regardless if the battery disconnect is on or off. If the battery disconnect is off and I turn off the inverter, the red lights will go out, very very slowly.
The step is connected to the engine battery, not the house battery. This is for safety reasons. You always want the step to come out, otherwise you have one great big step down to the ground. That could hurt.