A suggestion, if I may, for the version 2: make it remote controlled, with an IR receiver inside the car. No car thief uses a TV remote control.
I've considered that, or RFID, but really my problem is always running out to my car and forgetting my key. This way I don't need anything (remote, tag, key, fob) on me to get in.
Will you leave the option to open using the key?
Of course! I didn't remove any functionality from my car. To lock and unlock my car, all i had to do was close two wires already in the door together with either a 1k ohm resisitor (lock) or a 330 ohm resistor (unlock). I wired those with tiny solid state relays on the board. They are actually under the nano.
Here's another suggestion: make it honk the horn if the entered code is incorrect three times within a certain period. That should help deter tampering.
I'm not really worried about anyone brute forcing the password. I could make the code longer if I was worried. I'd rather not have the car make noise. Just my personal preference.
You want to look at using one of the external or pin change interrupts to wake the processor in sleep mode.
I've glanced over them before, but I didn't get a real solid grip on it. Maybe I'll revisit it in the next few days.