In general crabs are BAD in aquariums - there are some exceptions like cool little commensal crabs and such. I really doubt it could tackle and kill a healthy maroon clown - it is more likely the clown was dying or already dead.
If you want to catch him, get a small jar and put a piece of food inside, like shrimp. Lean it up against the rock where he lives. In the morning, you'll almost certainly have a crab inside you can't get out. The most humane way to dispose of him is to smash him or chop him in half very quickly. (Well, actually clove oil is the most humane way, but if you don't have any...)
No, bristleworms are not bad. If you get a lot of bristleworms, it's a sign your tank is too overloaded or overfed. Cyano is also a symptom of this (also it indicates, usually, areas of poor flow). Using an antibiotic is not a cure; it will do harm in the long run, so it's best avoided. The remedy is improved flow and more water changes.
There is no "cure" for brown jelly disease other than to help the coral fight it off, mostly with proper flow. For LPS corals like the Euphyillias (like the frogspawn) that means polyps should wave in the flow and stay aloft, but not be blown strongly in a way they cn get damaged.) Siphon off the jelly and give the corals a Lugol's (iodine) dip. For multi-headed corals which can be fragged without tissue damage, fragging off and throwing away the affected portion may help.
Yes, fresh fragging and then moving into a new, unstable tank is not a good thing. Ideally you'd let the frags heal in their old environment before moving them, but sometimes that's not practical.
Your blenny is probably not deliberately eating the coral, but rather scraping it. They feed by scraping algae off things. If the coral is weakened, there may be diatom films growing on it the blenny is actually trying to eat, but doing harm in the process. Or it could actually be eating the coral - it does happen, but it's more likely he's eating the algae. It's something you'll need to keep an eye on.
Again, photos will help. The frogspawn you just described does not sound like brown jelly. Xenia do not often get brown jelly disease - but they do melt when they die.
It sounds like you have had a tough time so far. Slowing down and practicing good QT will save you a lot of grief and money. Just hang tight with what you have for now until everything is under control.