Does the coolant reservoir have to have fluid in it?

yes, or should i say its supposed to. If your cars cooling system uses a expansion tank you have a problem on your hands, coolant should be flowing through the expansion tank on a regular basis(when the thermostat opens or closes). if you have a overflow tank, coolant flows in or out as needed by the systems heating and cooling cycles. If the radiator is low top it off then fill the resivor to the minimum cold level(shown on side of tank). But if your coolant levels are low you should ask yourself where is it going? if you cant find a external leak (around waterpump,bottem of radiator or hoses), then you might have an internal leak.