The mirror retrofit might be doable easily enough, as both mirrors have power to the blinking alarm indicator (a.k.a. clown nose). I can't imagine that there is a different wiring harness for cars with non-dimming mirrors.
I have retrofit an OEM dimming compass mirror on my wife's Audi, and found that the harness was there in the headliner, but the wires were terminated at a distribution block that led to nowhere, and I had to complete the circuit by tapping into some power in the footwell fuse box. I would expect something similar in the BMW too.
As for parts needed,
check here. There no prices, but I bet from the factory, you are dealing with $300 or more, seeing both incorporate the rain sensor and auto-headlight sensors too.