Newbie to MH - advice please

we have acquired a MH Autocruise Starfire 2006 - we have been through the books and need clarification on a few bits (may be obvious to some).  When connected to mains power, does this charge the leisure and vehicle battery whether or not the control box in MH is on/off.  There is a double battery symbol on the control box - when pressed and illuminated does this mean it draws power from the vehicle battery? Just a bit concerned as we had not used for a few weeks and when loaded and ready to go we had a flat battery and had to jump start.  When we finished up yesterday both batteries said they were 13.7/13.8 and today they have both dropped to 12.6/12.7 just wondered if this is normal or if we are leaving something on in error.  Thanks in advance for any help