you dont really need any mechanical filtration other than a skimmer (which i just realized you didnt mention owning) so the hang on power filter is really not needed except to occasionally run carbon to polish the water for a couple of days and then be removed again. if you want you can keep the filter minus any media for the extra flow it provides, personally i'd remove it from the tank, one less thing to worry about.

As for the skimmer, do you have one? if not you really should, especially since your are a beginning reefer, it'll make keeping the tank clean easier because it'll removed disolved organics from the water keeping them from fueling the algae.

As for your nitrate test zero is not unusual, any available nitrate is probably tied up with the algae being used as fuel. if you test in the morning just before your lights come on you may or may not be able to get a reading since the algae will have released some of the nitrate while the lights were out.

if your polpys do die, cut your lights and take care of your algae problem before buying anything else that is light dependent, it'll be easier. in the meanwhile you can cut your light back to 3 or 4 hours to help kill the algae off.