Not sure about the star, but definitely don't use straight tap water. Conditioned water is better but not 100%. Acceptable for freshwater tanks, not sw as they are much more demanding for good parameters to sustain life.
If you can't afford, or want to shell out a bunch of money on an RO/DI unit, you can get 5 gal of uv treated RO water at Walmart for $1.90 (37¢ a gallon plus tax) after you buy the bottle. There's of course no guarantee the filter is changed regularly other than the signatures on the quality card.
Start with identifying the root of the problem and work your way up, then you will know why the starfish is acting weird. Good luck.
This^
I can't begin to even narrow down potential issues with the star, the water quality you're using is a MAJOR factor, even when conditioned there is still possible pathogens that can end up in the water, including copper from the pipes!
I suggest getting your water tested for copper, and purchasing yourself a RO/DI system, cause you'll go broke purchasing indivigual bottles of the stuff.. but also because like above said, you're very reliant on the label of any sold products.. you don't know how careful it's processed or packaged. Instead of 99.9% RO water at home.. you can purchase 97% RO, 3% contaminated water.. which adds up.
LFS often can supply the same water and are usually much more reliable on handling it having the full understanding of careful handling and since it's specific on the hobby, they're not going to just toss it through any random copper pipes and not take it seriously like drinking water.
Oh yeah, 30g is really small for a CC btw. Indivigual is fine, but a foot diameter star will be a little difficult to fit when it reaches that size.
They have no brains so if you feel you must "dispatch" him then just remove and smash his center with something. They dont feel pain so anyway to "euthanize" will work. See if you can get him to recover though.
If I need bone cutters to detach a leg, then smashing it is not such an easy task

although I would remove it cause they are ammonia nukes when they melt.. and they stink. For me, at first sign of melting or "turning inside out" they go in the trash sealed air tight.