There are some people on here who seem to know more than even BMW about how these things work. Until they respond with the answers, some brief clues I can offer are ...
I don't think you're using the term
immobilizer as it is usually used. I think of that as the system that uses an RFID chip in the key that is interrogated by the ECU upon starting the engine, and the ECU will either allow start or not.
The
keyless entry system is separate, easily programmable by following a sequence of button presses, etc. That allows you to lock/unlock doors, disable the alarm (that would be automatically set when locking), and even roll down windows and open sunroof if holding down the unlock button.
The
alarm is separate.
The
mechanical key blade is the 4th fairly independent thing in this part of the whole security system.
I believe the clown nose indicates whether the alarm is armed. It is armed automatically when locking the car when the key is out of the ignition, whether done with the mechanical key in the door or with the keyless entry remote. If locking with the mechanical key does not set the alarm, it would indicate some issue somewhere in the whole system. And that is a major factor to consider - the system is pretty complex, and if one part (door lock actuator, for example) has a partial electrical failure, it can make the whole keyless entry and alarm systems inoperable. <== and that's exactly what happened to me.
If you can't get keyless entry to work, and rely on the mechanical key in the door to lock and unlock, you can be sure the lock cylinder will fail within about a year of daily use, leaving you in a predicament. <== and that's exactly what happened to me.
A cheap and easy solution to the need for a remote functionality is to buy a used genuine BMW diamond key on eBay (I bought 3x for $15 each when I got my car). You can then cut the key blades off (useless on your car), reprogram the keyless entry functionality, and use them as key fobs. You'll need to find a convenient way to keep them charged. When you go to start the car, the immobilizer system will see the RFID chip in your actual key as well as the old one in the eBay fob, and will just ignore the eBay one, allowing the car to start. <== All that is exactly what I've been doing since 2014.
