I'm actually having the same problem with you. I have tried different cables and cigarette lighter adapters on different cars.
I can confirm that neither charging nor aux cable works for me on the following cars: Mercedes C180, Renault Clio, Honda CRV, Ford Focus.
However, both the aux and charging magically worked on a Land Rover Defender (1973), connected to a mediocre Pioneer player. Also I do get a tiny bit of charge from the Merc's USB player port, probably for powering usb memory sticks, or players. But it is so slow it just slows the battery depleting rather than charging (better than nothing on a very long road trip I suppose, but I worry that it might hurt the battery in the long run)
I also do not get any music, if I use anything else than Sony's Walkman app when connected via Bluetooth. So i suspect this might be a software problem (perhaps to do with "throw" ?)
Anybody found a solution to these problems? Do any of you guys run the Z2 with a custom rom? if so, which one? because I'm thinking about installing a custom rom to see if that will help?