as above
1] the 12 v aux battery isn't charged by the engine, it is charged by the vehicle's low voltage supply which is provided by the hybrid system when it is in Ready mode. That energy comes from the high voltage traction battery, regenerative brakes or petrol engine as determined by the system. It isn't something you need to worry about or can control.
2] the petrol engine is started from one of the electric motors within the hybrid system, powered from the high voltage traction battery. The 12 v aux battery only provides standby power for retaining memory settings, the alarm and door locking/unlocking, and powers up the vehicle's systems to allow it to get into Ready mode when the hybrid system takes over.