I have not had volume issues with my CarPC's (today one in a 330XI and another one in an X3). I did not make my own AUX cables but rather just purchased them. In the X-3 ran the audio cable from the front HU to the rear of the vehicle to the CarPC which was a longer run than the 2 foot audio run in the 330XI. I would tend to believe that the volume issues are caused by your cable. I also would say that this is the best methodology to get to the audio in your car. My carpc application just displays in the AUX mode and all of the radio control mapping (both steering wheel and HU) work well with my music / video application.

On a tangent I have been experimenting with making a very small CarPC for the X-3 and during my "experimenting" noticed an audio hum from one of my test pcs. Just recently updated this same said PC to another MB/PS and the hum has gone away. I am not sure but believe its related to the 12VDC automotive style MATX II PS I used.

1 - Yes this is amplified in the stock amplifier
2 - no, I believe that AUX is best methodology. Originally folks were doing it via the tape audio input connections.
3 - If it doesn't see aux its your cable or the revision of your radio that doesn't have AUX mode. What model / revision radio do you have? Your 2004 radio should have AUX functions.

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E83 - Aero PKG Mods installed: Homelink mirror. CIS-IBUS video module, AUX, Rr Dr Release, stock wheels, Remote start, CarPC (Atom) & mud flaps - NAV - MKIV - NA Map DVD - 2011
E46 - 18.5 wheels/tires (summer), 17 stock (winter), Homelink, NAV software upgrade, BMW video module, Radio to V53, AUX, USB IBUS interface,BMW alarm install, CarPC(Epia), remote starter, tank battery & angel eyes. NAV - MKIII - NA Map CD - High Version 2008.1