charging batteries

no doubt been discussed many times before. my van is running on mains ehu and batteries showing full charge. the fridge is on. my question is, if i unplug overnight presumably the fridge will try gas power. or if i leave the leccy on will it over charge the batteries? thanks. Doug.

hi Peter. i am going to drive to camp tomorrow and was a tad dubious about battery charging overnight. the fridge is on and full. i seem to be talking gibberish but the handbook is not totally relevant to my van. thankyou for replying. Doug.

another minor snag. because our handbook  is not quite relevant to our neuvo its difficult to fathom correct procedures as regards the control panel. for weeks now i've assumed the solar panel is topping up the batteries. no reading on the control panel. over to the dealer for low down. seems the regulator was not connected at factory! 
i also checked the leisure battery, as i paid for 100 amp jobby. its still got the 60amp original. nothings simple!
not a splendid start for my ownership. at least the dealer is only 4miles from me.