Is the ZIG X70 Battery charger, thats built into my caravan also, the transformer that converts 240V power to 12V, when plugged into EHU?
I suspect the X70 is dead, as no LED's light up anywhere, and that this could also be the reasons the battery doesn't charger, and that the lights don't run of 240V EHU - and will currently only run off the battery.....
Yes, in answer to your first question.
You will need a multi - meter ( volt meter ) to check if the unit is working.
Simply disconnect the battery and connect the volt meter to the wires ( making sure they cannot touch ).
Turn on the charger unit or connect the caravan to the mains and the meter should read around 13.7 volts.
If it doesn't then either the until has failed or no 230 volt current is getting to it.
You don't say what caravan you have, which is always helpful, but around 2006 /7 Swift were fitting units that were prone to failure.
Incidentally, most, if not all, of your lights will only operate off of 12 volts.
Depending on your caravan you may have 2 230 volt lights usually in the front of the lounge area.
Good luck, DaveS1