You should consult the manual for your power station to answer your questions.
In my opinion such a power station does not make really sense, because the 720Wh (if full) will give your house battery an additional amount of 60Ah of energy (compared with the standard house bank size of 140Ah).
Due to the fact that the power station contains Li-Ion cells i would assume that the risk of fire is higher compared with lead or lifepo4 cells.
I would go with a standard mppt-charger for the solar panels and an inverter capable for the needed power. If necessary, i would add another battery to the house bank.