This has been bugging me for ages and i'm glad I checked this thread. I have a Nissan Note 2014 and I've been having exactly the same issues listed.
I avoided jumping on iOS 8 straight away as there are always teething problems after launch. Eventually, I got on board with iOS 8.2 and that was a big mistake. Ever since then my 5c has been driving me nuts when connecting in the car. I get constant connectivity problems, meaning it won't play music or even charge. I also noticed it appears to always be on MIX/SHUFFE despite me not putting it on that setting. Music won't play, despite it listing my albums/artists etc. I even tried changing the cable but the same problem occurs.
Never had any problems previously with same phone/same car. This isn't really a Bluetooth issue, as the music plays via USB. Definitely a device problem, and definitely a iOS 8 problem. 8.2 still has this bug. Please pay attention and acknowledge Apple.