I think (but I'm not sure) the remote fob doesn't work when there's already a key in the ignition because locking the car via the remote also switches on the immobiliser. So I don't think there's anything wrong with the key fobs.
On my old 3 series, the alarm and immobiliser didn't engage if you locked/unlocked via the keyhole. Also, you couldn't lock yourself into the car by blipping the keyfob once the key was in the ignition, but you could lock all four doors from a switch on the driver's door. It seemed to be a 'design feature', not a glitch.
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