I think you do a good job of describing anarchy. The one thing I think you could do better on is religion. You try and say all religion is the same and is just God telling people what to do. While there are some religions today that have a central person telling people what they can and can't do, this is not an accurate description of all religions. For example Buddhism is more about meditating and thinking about life questions. So, while some forms of religion are incompatible with anarchy, I would not say that all are.