portable battery charging

and in the meantime, can I connect the battery charger to the battery while the battery is connected as normal? So we can use our 12v system, Fridge, lights, etc.,

Yes,I do it all the time when boondocking.After a few days the system can't keep up with the draw when just plugged into the generator for a couple hours a day, then I hook up the portable battery charger to the batteries on the trailer in place.Just pop the battery cover lids and hook up your charger to increase the charge and in a short time, your back to full charge.