Q: When I turn ignition off and pull key out, car doesn't shut off. when i can shut it off, next morning battery is dead.

Malfunctions in the EGR (Exhaust Gas Recirculation) system would not affect the ignition system or battery. If the EGR system has a fault, the service to request is EGR system diagnostic/inspection. If your vehicle engine continues to run after the ignition switch is turned off that means the ignition switch is defective and/or the ignition is still being powered from "elsewhere" in the circuit even though the switch is "off". If a new battery discharges overnight, when the car is not running, that means there is a phantom electrical load(s) somewhere that will have to be identified and repaired. The magnitude of the phantom load can be discovered by inserting an ammeter in series with the battery and reading the power draw. To then find out "where" the load is, main circuits are traced and once the search is narrowed to one main circuit, the branches are tested sequentially until the circuit(s) with the fault (the phantom load) is found. If you want these steps performed by a certified Mechanic, dispatched by YourMechanic right to your location, please request an electrical components diagnostic and the responding certified mechanic will get this resolved for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.