Don't know if this helps but with the ignition off and keys out, all the relays in the fuse box are still energised ( which I think is wrong) this is one of the causes why the battery goes flat quite quick compared to other cars. Best thing to do is use the circuit breaker when charger is connected. It could be one of the relays faulty, removing each relay in tern gives all sorts of weard effects. Have found this out on my 2008 S4.
That is very strange. Surely, when the ignition is off only circuits associated with any central locking, tracking and/or immobiliser need to be active.