I don't think i'll be able to answer your question about "power" throughout history but I can speak to how geography affected the development of early settled civilisaitons. Egypt is a great example, yes most of modern day egypt is uninhabited desert, but it is not in the desert where the two Kingdoms of Egypt (which eventually combined into one) developed. It is around the Nile river, if you look at a modern population density map of Egypt much more than 90% of the population lives along the Nile river and the Nile delta. What made the Nile so fantastic 5000 years ago is that it floods regularly every year (not anymore because of the aswan dam), this flooding deposits highly rich silt next to the river, resulting in incredibly fertile land for which to grow crops. You see similar patterns in other places around the world where larger scale civilizations developed, Mesopotamia with the Tigris and Euphrates, the Indus valley with the Indus river, and the yellow and Yangtze river in China. I can't speak for your other points but at least in the initial development of civilization more than 4000 years ago regularly flooding rivers were highly important.