If I recall correctly, ich, as with many other fish parasites, is always present. Healthy fish are quite able to combat infestations without the aquarium keeper ever knowing it is there. Healthy fish are stress free fish. 3 tangs in what amounts to (by the looks of things)15 gallons of water (think displacement) would need weekly water changes at the barest minimum. Although they are eating and appear happy, proper stocking is generally based upon the adult size of the fish so yes, you will constantly get spikes in nitrates etc.. Basically, keep 5 gallons of fresh mix (powerhead and heater to match tank parameters) made up at all times and test parameters daily . Using this method, you can kep your system running without a filter indefinitely. I would however re-home those tangs asap and a protein skimmer can't hurt.