Mucus description sounds like a spaghetti worm. I wouldn't be worried about it. As for the asterina stars, if you don't see them on coral, I would leave them be. Mine seem to only care about film algae, but there are many species of them and some are definitely reported to eat coraline algae or actual coral.
Melting corals is most often salinity in my experience. Ruling out salinity, the kenya and pineapple corals are possibly fighting which is why they look like crap. Soft tree corals are very prone to using chemical warfare on nearby corals. These chemicals are designed to irritate or stunt or sometimes completely destroy competing corals. I had a xenia and kenya go to war on eachother in a previous tank, and I eventually had to get rid of one. Running carbon can somewhat help, but IMO if they decide to fight in a tank this small, there may be no choice but to remove one.
Anyway, I wouldn't quite go there yet. I think you're just hitting one of those new tank road bumps right now. Tanks this small are often difficult to maintain stable parameters Based on your previous post, I would still suggest staying on a routine schedule and make sure to closely match your parameters before doing > 10% water changes. I think this is one of those diligence and patience will prevail moments, unless you do find something measurably wrong with the tank.