re: Waste not.
You have two hydraulic options - continuity and discontinuity.
In a continuous system you have thick-walled high-pressure trunking that pumps water to the top of the building. You need pressure reducers at all the intermediate taps off this, or the washbasins will shatter from the force of the water jets.
Oh, and you need some good plumbing to stop the toilets on the 90th floor escaping on the 10th floor!
Alternatively, and more normally, you simply have a chain of smaller hydraulic units, discharging into reservoirs (tanks) every 10 floors or so. So you only pump up 10 floors at a time, and flush down 10 floors at a time.