Yea, there is an issue with the head missing from the rigify rig. I tried to configure the avatar in unity to adjust for it (manually selecting the bone, which in this case is just 'spine' - since its not named head I imagine thats part of it) but after that, since the "head"/spine bone I select isn't a child of the "torso/chest" spine it results in other problems.
As I mentioned, I'm not super familiar with rigify so I can't speak to the finer details of the issue(s) with the rig. I tried to 'optimize for unity' the rig in Blender, but that only resulted in other problems that weren't caused by you directly so I can't knock you for that.
Do you think you could upload a non-"rigify" rigged version if you get the time? If not, its fine- I can probably get it fixed some time