Yes, Moto C comes with removable battery.
No. Auto Call Recording is not available but you can download Auto Call Recording apps from the google play store and can do auto call recording.
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 expand the memory by up to 32GB with the help of MicroSD card.