Sea fans are not easy to keep. These are non photosynthetic corals and require daily feedings. Your experience sounds like a classic case of them being starved to death slowly.
What sort of LEDs are these? 3W, any optics? Sounds like you have alot of light for your small tank. Not all zoas need strong light. Many of them prefer low-medium light.
If your temperature is at 30 degrees regularly, that could have contributed too. Corals typically do better below 29 degrees.
Don't assume that nitrate is low. Test for it. Same as iodine, calcium and strontium. Do not add if you don't test. Otherwise you might overdose, and it might be lethal. Since it is such a small tank, you have to know how much to add. Corals are sensitive to major fluctuations.
There is no such thing as wrong tester. Just buy all the kits if you want to. Otherwise, just get the basic ones first like Sherman mentioned.