Your avatar body can be killed and the human driver will live. The brain goes nuts for a little while though. You see Norman still clutching his chest and panicking, after he is shot, even though he'd gotten out of the link and had scurried across the room. The brain needs time to recover depending on the trauma.
As for Norm's avatar body, we don't know what has come of it yet. There are still handful, maybe even a few dozen humans, mostly those in the avatar program, left on Pandora (the Hells Gate region anyway). I'm unsure whether Cameron is going to convert them all to Na'vi like Jake, or if they are going to have to maintain the link rooms. My guess is that they are going to maintain the link rooms. We may never see Norm in avatar form again, but I doubt that.
You see Norman at the end in his human form. His Avatar may still be out of commission from being shot, or possibly just an attempt to reenforce the fact that Jake is now a full-blown na'vi. I'm assuming the Na'vi are going to help the humans fix Norm's avatar with some Pandora medicine or surgery techniques.