I can't really see what's wrong with the fish since I don't know which fin to look at xD And I can't find any black moor in the photos in the first place d: But I guess you mean the telescope eye there (Really beautiful!)
Either way, if you say that it looks a bit moldy? I would say that it might be a fungal infection, possibly with some fin rot. So I would separate him and start treating with anti-fungal and -bacterial meds You could try Melafix and Pimafix for now and see if it works. They are natural remedies so they're rather to help the fish recover by itself than to actually kill off any bacteria. You could try these for a few days, and if they don't work, try buying something stronger, still for bacterial/fungal disease.

If you want, you could add some salt along with the Melafix and Pimafix Salt works pretty well against fungus too, and it's like a tonic for the fish

It looks like it might be a wart.
 I would check at the pet store to be certain. Bring them a sample of the aquarium water in too so they can see what the water quality is.
Have you got a filter?
 It could be bacteria  though.
One thing that you should do (Other people have written this on the site and they have said it works!),
is to give him a salt bath. Don't put in to much salt, and as i said, it is probably best to ask the pet store.