I've been here so let me see if I can help. The problem is things can go wrong for so many reason, so its really a process of elimination. Some of those fish may have died for different reasons too so that makes things more complicated. Unfortunately it may take awhile to find the problem. I would highly recommend taking some tank water to a local pet store to have it tested for you.
Here are some questions to consider: The fish that lived for 3 weeks, was anything different in the tank for that fish? What kind of rocks do you have? they seem to have algae on them, so they are probably fine, but do you know what they are? Do you top off water with RODI water or from the tap? how often do you change water and the carbon in your filter? What else does your filter have in it besides carbon? How often do you change those things? When your fish die do you see spots or powder on them?
Here are my guesses:
1. Disease: Maybe you're getting fish that are sick. My guess with dying that fast it would be velvet. Velvet can also be hard to see.
https://www.reef2reef.com/threads/velvet-amyloodinium-ocellatum.217570/. But that is just a guess! If it is velvet you'l need to leave your tank fishes for 6 weeks to ensure its gone from the tank. I might suggest also getting a fish from a different fish store. At least if you can try that once it might be good for the process of elimination.
I have noticed that they tend to clamp 1 pectoral fin and I don't see any movement from their pelvic fins... Maybe this is a big give away?
2. Ammonia spikes: The dying snails could be increasing ammonia in your tank, and adding a fish in conjunction with a snail dying may be causing brief ammonia spikes that are deadly. The ammonia could be converted to nitrate by the time you test the water.
Plausible...
3. Toxins: Maybe the skull or the ship really are the problem. I've seen tanks on this forum withs skulls so there definitely are reef safe skulls. Perhaps your skull or ship have a curse on them.... In any case just to test it I would remove them, perhaps do a water change and add fresh carbon and let that run to get any possibly leached toxins out, then swap that for new carbon after a few days and see what happens when you had a fish. Does someone clean around the tank with windex or light scented candles around the tank? (Those should affect the corals too though).
...as noted... Corals and Shrimp are healthy
4. Acclimation and Salinity: You are using a hydrometer to measure salinity, perhaps it is faulty (although I'd think corals would be killed before damsels if your salinity was really off). Do you know what the salinity of Petco's water is? Perhaps it is different from your tank. You could try acclimating your fish by first floating them with the lights off for 10/15 minutes and then opening the bags, and taking out 1/5 or so of the water and replacing it with new tank water every 10-15 minutes until the water has turned over. To me that method was always easier and less intimidating than the drip method. Are you adding the water from the bag to your tank? It is usually suggested that people avoid adding any bag water to the tank.
Their salinity is between 19 and 26
5. Another possibility - are you feeding frozen food? Perhaps it unfroze at some point and is rotten.
Freeze dried and flakes
I hope my long post helps you somewhat! Good luck!