is it good to attach an extra battery parallel to a small-inverter system
As I see it, you have a 12V battery with a 8 Ah capacity.  The simplest way to increase its capacity is to replace it with a higher capacity battery. Kinetik Audio (at www.Kinetikaudio.com) makes several types with different capacities.
If you want to use several batteries, then you need to "protect" them by using one diode per battery (to the common rail) to prevent the batteries from recharging each other.  The drawback is that the load current is limited to the current capacity of the diodes.  Also, the charging capacity of the charger may not be sufficient to recharge the batteries in a "reasonable" time.