2. The grid mostly doesn’t care how far the battery is from the panel.
3. Lithium ion is an incredibly inefficient means of storing power that doesn’t have to be portable. Grid storage doesn’t use Li ion because it isn’t cost effective.
In summary the major misallocation of resources is using lithium batteries to store grid power at all. At home solar is the next Great Leap Forward for humanity. It's about as logical as making steel at home.
In case you didn't get the reference: https://en.wikipedia.org/wiki/Great_Leap_Forward
It's not hard to calculate the economics of batteries for residential solar (I've done it repeatedly), but I can save you some time: it's pointless. Because if it was viable, then it would cheaper and more efficient for utility companies to build their own grid batteries (which they do: but not for long-term energy storage, they use it for grid stability).
The price you pay for off-peak power, will always be slightly less the minimum cost of battery ownership. Because if batteries were cheaper to own, then you would get that price via your electricity bill anyway.
Mass, doesn't really matter unless we are over what single truck can deliver or can be installed at time. Meaning tens of tons.
Volume, some limits, but still I think few cubic meters is in reasonable space. Compare to oil and gas.
Cost per kwh and cycles is the important ones. They should result in less than grid costs.
Also I would consider safety to be important. Is there risk of fire? In event of fire does it keep burning? Does if off gas something toxic that stays also after? Etc.