There is kWh per day,
kW continuous load,
kW peak load starting motors.
The batteries will have similar specs, but in the form Ah, A continuous, A max for a limited time.
You will need some number of batteries to supply the kWh per day, but possibly a larger number for the starting surge of something like an A/C or pump.
When you connect a lithium battery to an inverter, especially a several kW inverter, for a moment the input capacitors look like a short circuit and it draws thousands of amps - way more than battery's BMS wants. This can cause battery to shut off, or for fuses to blow. To avoid that use a precharge resistor.