The battery is 16kWh. Effectively around 14kWh, since you never fully discharge. LiFePo4, so no chance of spontaneous combustion like other battery chemistries.
I'd say the months Nov→Feb are tricky, although since I have quite a bit of excess solar capacity there are even in December plenty of days where the battery pulls me through the night.
Charging/discharging from/to the grid is possible, since I have a retrofit inverter (AC to battery), but not doing it yet, have to do a bit more research (dynamic pricing, tax is >50% of the kWh price in NL, etc).