How much power does the power inverter need from the batteries?

As a rule of thumb (leaning on the high side), an inverter will require 10% of its continuous wattage rating from a battery. Example: A 300 watt inverter providing 300 watts to an appliance will require 30 amps from the battery. The same inverter providing 150 watts to an appliance will require 15 amps from the battery.