This is the blind leading the blind, as I've only fitted one Zappi PV system. Can you find a manual?
But in terms of concepts....
Think of a normal supply and consumer unit.
Normally either
1) a way of the consumer unit will go off to the inverter (not great design).
2) there will be split tails and a separate consumer unit and a circuit going off to the inverter (the right way).
DC electricity falls from the sky onto the panels using witchcraft, and the inverter turns it in AC and back-feeds it into the supply using the same connection referred to above.
The batteries get charged when there is "spare" generation that the installation usage can't swallow. The batteries let themselves be used in a moderated way so the stored energy contributes to the supply.
But basically it should be one connection via a consumer unit to the whole shebang which both powers the inverter and accepts the generated / stored electricity.
As far as I'm aware inverters actually have to shut down if the grid supply is lost. So if there is a power cut you still have a power cut (which must be rather frustrating!).
In that installation I'd start by analysing the normal supply, consumer units, and final circuits, and that will lead you by elimination to how it's connected - I'm sensing that convention may not have been followed!
Be aware that the DC lines from the panels can be live at all times, and hopefully you will find an isolator for them somewhere.
That looks such a mess that I'd be in ultra-suspicious mode!