Most of what you described appears to be learned behavior. This child is seeing and experiencing a lot of things that she should not. It could lead to some sort of mental problems down the road but it is hard to tell right now if it is contrived behavior or learned behavior. It seems learned to me and from the description of her mother, it likely is but if she does have any mental problems, it makes it harder to tell and regardless of the origin, the actions are unacceptable.