There is a lot of liability in sticking your name on a hodge podge of random used lithium cells.
Weight is not a factor for home energy storage, there is no need for lithium cells.
That depends on your living situation. I live in a third-floor apartment, so weight is very definitely a factor.
If you reduce the energy density by a factor of 10, the weight for power backup needs will still be far lighter than the concrete.
But I do think there should be home energy storage that doesn't involve chemical batteries. Where are all the pumped hydro, flywheels, and compressed air storage for consumer use?
Larger batteries, including some electric cars, have switched.
https://cambridgerenewables.co.uk/product/eleven-energy-4-5-...