My first comment will be that you eventually need to get away from tap water and either purchase RO/DI water or buy your own filter to make your own. I can't say that it would cause your current problems, but it could lead to issues in the long run. The problem with conditioned tap water is that they only absorb the "bad stuff" in the water where as RO (Reverse Osmosis) removes them from the water. If you have copper pipes in your house, you may run into issues with your inverts as copper is lethal to marine invertebrates. RO/DI water will insure you that the copper is removed from the water source.
I will also say that your tank is still very young, and you may experience swings in the parameters. You will also probably experience many algae blooms typically with a new tank. I left my tank fish free for over 3 months. I know that's probably overkill, but patience is key in this hobby.
As for the fish, you may have simply bought a sick fish. I would leave your tank alone for a few weeks and observe the tang closely for issues. I personally wouldn't stock a tank that size near as fast as you were recommended. 2 fish a week can add a bio load too quickly for a smaller tank IMO. I've always gone by the "add a fish per month unless you're adding a pair" rule on my 55 gallon.
Another tip is to always quarantine your new fish. Since you bought your first two fish together, this doesn't make much difference, but consider in the future if you have $500 worth of fish in your tank, and you buy a sick fish and put it directly in your display tank. The sick fish gets all of your other fish sick, they all die, and you're out $500. It's recommended to quarantine all new fish in a separate tank for at least 3 weeks prior to introduction to the display.
I know that's a lot of info, but I hope it helps. If anybody sees anything where I misstated something, please correct me.