Can I use the 12 V power in caravan to drive for example the lights, whilst the battery is being charged by a mains power charger? By the way, The 12 V system is on a separate circuit to mains power. For example, if no mains power is connected to the caravan then only 12 V items like lights and the gas stove ignition button works. When I connect mains power then I have power to wall sockets and the fridge too.
Yes you can. The voltage across the battery during charging will be a little higher than usual but most caravan type accessories will cope with this.
If in doubt check the highest voltage the accessory will work at and the highest specified charge voltage for the charger.