Where will you mount the sub amp? Power for the amp needs to come directly from the battery. BMW did us audio mod’ers a favor by adding a lug with a nut on the red positive battery cable. I’d run the power for the sub amp from that lug. Do not use the battery’s black ground/earth/negative post fir ground as you’ll get a huge amount of electrical noise. Ground the amp at the audio ground lug forward and above the factory amp’s location.
Does the sub amp take line level (aka RCA) signals or speaker level signals? Is the sub amp designed to power just subs or is it a full audio range amp? I ask as if the amp is a full audio range amp you’ll need to install electronic components to block higher audio frequencies. Why? Sub woofers don’t like higher frequencies.
The turn on wire in my departed 2001 330Ci was cream/off white in color.