You choose which Beast is fighting which creature an opponent controls.

If Ezuri's Predation creates more than one token for any given creature (due to an effect such as the one Doubling Season creates), the extra tokens won't fight any creature.

Players can't cast spells or activate any abilities in between the Beasts entering the battlefield and fighting the other creatures. If the Beasts entering the battlefield cause any abilities to trigger, those abilities will be put onto the stack after Ezuri's Predation is finished resolving.

Each of the "fights" happens at the same time.