Can I use two inverters of 220 V (500 W) on one battery at the same time?

You want to have a common battery. Have two batteries in parallel, and have a one-tenth ohm link between the two. (make sure the one-tenth-ohm link can handle the differential between the two batteries when one goes lower than the other.) IE one battery is full, and the other battery is only 20%. This will give a voltage potential of 10V across 1/10 ohm or 100A max. By having the 1/10 ohm between, then the voltages will drift as appropriate, and charge the entire system. But beware, some chargers cannot adjust to 2 batteries in parallel. Two Inverters, two chargers, two batteries. Make sure that the chargers can handle two batteries together. There are devices that will block current, and back current from going the wrong way