It doesn't sound like it was cycled in advance (one piece of live rock just isn't enough), so then when fish were added, ammonia spiked and killed some of them. It is likely ok now, but as the fish mature, it's going to be crowded and overstocked (the unnamed blue fish look to be a damsel, which are nasty tempered even in large tanks). Clowns are in the same family and equally territorial. I'd take the damsels out, and leave just the clown, goby and shrimp.
And the skimmer is working overtime because there are a lot of wastes in the water. Are water changes being done? how often and how much?