Yes, one of the things that gets glossed over many times in this field (I used to do research in artificial photosynthesis) is that water gets consumed to create the fuel, and is released as vapor from every engine's exhaust. So to generate 10 million barrels requires about 10 millions barrels of pure water, per day, to satiate the US.
Yes, water is turned into fuel and oxygen. In most places the water can be obtained from moisture in the air (there is much more water than CO2 in air, and we are already mining the air, so we can get both). In the process the fuel is separated from the water, which remains in the reactor, and is topped off as it is used to make the fuel. No waste water.
I think the water that is still there after distillation will just be used for more distillation, it just hasn't been consumed yet, it isn't a waste product.
