On #2

Carefully pry out the central locking switch from the center console and see if it is broken at the bottom. The switch housing is made of plastic and if breaks (which is common) the switch stops working and disables all central locking. If it is broken you can glue it back or replace it.

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'99 E39 528i 5-speed 130k
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'03 530i - manual swapped - 430k miles-SOLD