The Arduino has a linear voltage regulator which takes the 9V and burns off four volts at whatever current the AVR takes as heat.The rest of your question, I didn't understand. 600mAh (note the spelling) is a measure of the capacity of the battery. In theory, the battery could supply 100mA for six hours, but this is unlikely. It can probably manage 10mA for sixty hours.
and about the capacity, why its unlikely?