How long 1 kilowatt hour would last is a difficult question - depends on how efficient the home is and what tasks need to use that energy (for example, AC is very expensive but tends to be needed most when solar energy is available). Heating and cooling are most expensive.
Our energy usage in a not particularly well insulated home but in a subtropical Spring averaged about 9kWh/day - so 1kWh (3.6MJ) wouldn't get us far - it probably barely powers the fridge! However, you'd only need the storage overnight, and use solar energy the rest of the time. In sunny climes, at least.
Again, how much water depends on how much vertical drop, but it would likely be a lot of water (if you sat one cubic tank with 4.4m sides on top of another then emptying the top into the bottom would theoretically generate 1kWh)
