One of the reason for flash light not to work is due to the failure of camera.
Back camera on my iPhone looks blurry, do I need to replace the camera?
Make sure weather the lens on the camera is broken or not , most of the time when the lens break the dust deposit and damage the camera that's how it give you blurry image. In this case you need to replace the camera and lens as well.
The front and back camera on my iPhone doesn't work, are they both one unit, how come both fails same time?
The front and the back camera are separate units You are right, both units cannot fail at same time unless an accident happens.
Once the camera changed on my iPhone, does my face id works?
It depends how badly is damage, if it just cable ripped than it can be fixed.