Ok so this is actually something I can assist people with. Being such an Apple fan, I too experience this issue.
This issue is part Ford and part Apple. If your Fiesta has Bluetooth, you will notice every time your stereo is on your iPod function on your iPhone will be playing music. This is an Apple issue, and all cars with Bluetooth experience this. Apple deny that the problem exists, but so many people all around the world have this.
Your issue with your iPhone not playing music is a Ford problem. Because the Fiesta can play both via Bluetooth and the USB function via the Y Cable, it gets confused with what function to use. By default, whatever function is active first will play for a few seconds, that is if your iPhone is connected via USB it will play for a few seconds until the Bluetooth kicks in and all of a sudden the music stops, but it says the song is still playing. You need to open iPod on your iPhone, press 'Ford Audio' right at the bottom, and then select 'Dock Connector.' This will enable you to play music through your iPhone via USB and control it with your steering wheel functions. This works sometimes, as again the unit can get confused with the Bluetooth. iPhone doesn't know where to send the signal. Sometimes it'll display the song as playing, but it's not playing, sometimes just freezes and says the song is something like 18 hours long.
Best way? Turn your can to accessories, wait for Bluetooth to connect, then connect your iPhone. That way your saying to the iPhone and Ford Audio to override the Bluetooth song playing, and use iPhone via a Dock Connection. You will have full control with Voice Control, you're able to access playlists and control your iPhone via the steering wheel. This will work 99% of the time. You can still make and receive calls, sometimes it won't connect after though, you need to open your iPhone, select iPod and made sure it's connection via Dock. If this fails, disconnect and then reconnect. Make sure however that your in the Radio function before disconnecting.
Now when it says 'This device is not made for iPhone' select 'No' and continue as usual. You may need to change the connection method in iPod (Ford Audio or Dock connector are your options here).
iPhone has a few issue with all Bluetooth modules, but after you get used to the behaviour of the iPhone and the Ford Audio unit, you're fine. Please do not hesitate to ask a question if you guys need some help. Others have helped me many times so I'm more than happy to assist.