I am not sure about your algae issue with the cyano but cyano is caused by a number of things. It is easy to get rid of with something called chemi clean. I love the stuff and it relieved my cyano within HOURS!! I struggled with the manual remove, water changes and phosphate removal. Nothing helped til I got this stuff. It's worth the money and it's definitely worth a try if you're sick of no progress.
I bought mine here online at SWF.com. It's about 20 bucks, don't pay anymore than that locally or online. It only takes just a little so buy the small size.
On to your fish-
That infection looks pretty bad. The fins have started tearing and the fish looks far gone. Fear not, if you take care of it properly, you can probably save the little fish.
That QT is quite small, I would suggest putting the fish in anything else. In the past, I have used a 36 gallon rubbermaid bin that I had laying around. You know the ones you buy at target for like 10 bucks? I stole one from my garage that had Xmas decor in it, popped in a heater (warmer water is better for a QT) and then popped in a power head. Also, any light will do, I have very little light in mine... More light stresses the fish.
I have never used melafix, so I am not what the specifications are or what it's for. I would suggest going to ***** or petsmart and picking up some Maracyn 2. It has to be #2 as that is for saltwater fishes. There is a picture of a powder blue tang on the box. Does that as recommended and make sure that you double dose the first day. Every day you will need to do a 10% water change in the QT, before adding that days medications to the tank.
NEXT- Contact BETH on here. She is the fish medical guru. She has taught me a lot and saved countless fish. Just send her a PM.
Good luck.