I'll just add that you made a statement that, "...the kidneys are not receiving enough, or receive no water whatsoever? How long can one go without water?"
I think you've missed a huge and simple fact, you are only considering "external" water.
How does a camel survive in the desert? He's got a big bump (or two) of fat that stores water.
Our bodies are supposedly 70% water. If you consider that most people are 10% fat or more, that amount of water is certainly expendable. A small person, say 100 lbs, would then be 10 lb of fat. If 70% of that is water, that's 7 lb of water or nearly a gallon. This does not include all of the rest of the water in our bodies which is another roughly 8 gallons.
Obviously, the fast can't utilize all of the water, much is essential, but the point is there is already a significant amount of water "on board".
During dry fasting, the internal water is conservatively used. You will continue to urinate during a dry fast.