Always seems hard to know for sure. Basic speculation based on some limited experience in order of likelihood (more votes would help).
If that's a red spot on the six line I'd guess Lymphocystis (would be viral wait it out). I've had fish fully recover with those bumps. Typically haven't had frazzled fins though.
Either nipping or fin rot on the other 2 (but it doesn't seem like it'd be on the dorsal if it's nipping). Flukes in the realm of possibility. I believe praziquantel is reef safe and a quick fix if you suspect flukes. If you have tube worms they wouldn't make it and you would lose some worms/fauna. Fresh water dip would reveal them. Even just a minute or 2. I guess this could explain the tang's erratic behavior. Might be worth a dip.
Assume that's a red line wrasse transitioning male-- looks a little washed out. If that's just the picture and no flukes, I'd guess bacterial. I'd use mixture metro and kana plex bound to food with seachem focus. Reef safe in this configuration.
If you pull the fish to a hospital tank you could also add Furan 2.
Also if the wrasse was really old (4-5 years for a redline) seems like they start to get frazzled.
If he is washed out and young, you might have fish TB. They can live quite a while with it and it's incurable in a practical sense. Encouraging that they're eating. It's kind of weird you're getting it all at once, and the bacterial stuff doesn't usually jump fish too easily it doesn't seem. That's why I'm wondering if it's flukes even though the presentation is atypical.