Water rights are extremely complex, even if just looking at the United States. Water rights from a global perspective could fill up a textbook. In a very simplistic sense, no you can not use a stream however you want. Maybe if it doesn't leave your property, but otherwise you will have to be mindful of a whole host of issues, such as diminishing use for someone down river, altering the flow, pollution, impacting wildlife (such as endangered species), and potential impacts to wetlands, etc. These days, a lot of uses as well as construction, on or near, a river require permits.
While 71% of the globe's surface is water, only around 3% is freshwater, and of that freshwater only about 1% is surface water, around 30% is groundwater and the rest is ice caps and glaciers, and then again, most of the surface water is ice or snow.
In short, for every 15,000 drops of water on the planet only 1 drop is liquid water contained in lakes and rivers., which makes it an extremely valuable resource.
As for morality, who knows. Every other necessary good is priced and sold (even air in a way), so why not water?