How long have you had the fish for?
If it appeared overnight that could be an issue. My concern is the first picture in post #1, the black bit looks like it is coming out of the spine. If that is the case, then that is a concern.
If it has been growing in the muscle tissue for a few weeks or longer, then it's probably a parasitic worm that got lost in the fish and ended up in the muscle in the fish's back. If this is the case, there's not much to worry about and the worm will live there until the fish dies. You can sometimes kill these worms with Praziquantel, Levamisole, or Flubendazole, but most of the time the worms are unaffected by medications.
I would monitor it and see how it goes.
As for the fat belly, it is probably eggs.
If you haven't dewormed your fish, you could do that and see what happens, but you don't need to euthanise the fish or quarantine it at this stage. As long as the fish is eating and swimming around normally, just let it be.