Hi,
We need those test result numbers. Re-home the tang, your tank is way too small to keep any tang, a 55g is a very small SW tank. As a yellow tang matures it will become aggressive and start killing off the competition ... AKA, other fish that want's to eat the food, and hang out in his 6 foot mandatory territory.
The surface water breaking is fine, but like Beth said, you need circulation of that water throughout the entire tank. From your description of the fish in distress, the problem is oxygen, from either an ammonia spike (caused by overstocking, too many fish at one time), or lack of circulation of the water.
Everyone has their own way of doing things, and some folks insist a skimmer is a must have piece of equipment. I am of the opinion that all a skimmer does is remove organic waste, it doesn't oxygenate the water...although it will stir up oxygen, that isn't it's purpose. You don't have to have a skimmer, it removes the organic waste, and helps curb how much nutrients are in the water to feed corals, filter feeders and nuisance algae, most people overskim and waste their coral food additives. At any rate, I don't think a skimmer will fix your problems... but another power head will certainly be a plus, set it low in the tank to circulate the water at all levels.
Anemones are beautiful, however they eat anything stupid enough to get too close, and what they don't eat, they sting to death. They also can go mobile, they have no eyes or even a brain, just a mouth and an anus. They follow the water flow, and will get sucked up into the intake tubes and commit sushi, poising the tank as it dies. So cover all intake tubes and power heads. The type of anemone you have requires powerful lighting to survive, if you don't have heavy duty lighting, it will live for a short time, and then begin to die a slow death..