Yes, Motorola Moto C is a dual sim mobile phone.
Moto C has a decent pair of the camera on both the sides. The rear camera has 5.0 MP resolution camera with Autofocus and LED Flash. There are many other options available like beautifying software, HDR, Burst mode,etc. The front camera has 2.0MP and HDR support. The front camera also has LED flash and you can also use display screen as flash.
Yes, you can. But right now back panels are not available in stock, since the model is just launched.
Yes, Moto C does have a 3.5 mm music jack.