That's generally indicative of ammonia burns but I see you tested and you have 0.. You do need to be doing weekly and not every other week water changes between 25-50% and that should keep the water quality a lot better and you should never need such large changes.. but I'd test anyway with the snails just to be safe.
Snails won't hurt them directly but they are very dirty and can muck up the water quality and that can lead to things like fin rot. I'd remove as many as you can see and keep at it until they're all gone. Snails will eat live plants and algae..
Sometimes poor diet can lead to thinner fins and problems like this. I don't know anything about your pellet so I did a search and found this: http://www.bettafish.com/showthread.php?t=123475
Maybe try another quality pellet.
Also they could be getting snagged on something? The panty hose test is the definitive test. Take any ornaments and plants and drag the hose across and if it snags them it will snag your boys.
The lethargic one may also be stressed by the other which has asserted dominance and no longer feels threatened. Make sure your divider is opaque and try to put lots of plants and things up against the divider so they can't see each other. If that doesn't help they may not be able to live next to each other. At this point I would put poor sapphire in a QT where he cannot see Cobalt and see if he does better away from the other.
Generally speaking, for minor fin rot 1 tsp per gallon aquarium salt preddisolved for up to 10 days is a good first stop treatment and will fix most issues. Stress coat at 1 ml per 1 gal can help them grow back faster once the rot is under control. If you are worried about it moving too quickly or other problems, like Sapphire's behavior, a good antibiotic would be KAnaplex or Maracyn Plus (not to be confused with Maracyn or Maracyn II). Why do you think Sapphire has a fungus? It sounds all bacterial to me.