Hi did you have this battery coded, if not the BEM will continue to charge at the same rate as the old battery which in record time will cook the new battery and kill it stone dead, seen a few like this in my time and its hard to convince people of the importance of battery coding, half an amp is not an unusual amount and if the battery is in good condition its sustainable, the batteries are massive, damage wise 10-11 volts will kill it. the Adblue control unit is b@ll@cks they either work or they don't as for powering down the whole car never does this as there are alarms, central locking. infotainment all in a low power sleep mode until you hit the unlocking button.