No. Absolutely not. That's a normal fin. Actually the black extensions are also know as "trailing fins" You will see fish that are in the process of attracting a fish of the opposite sex get them. It's also a great thing to see on a show fish. It's a very good sign...and it looks great.
The melafix you are going to add, won't hurt the fish. It's not a bad additive...however people have a variety of opionions about its benefits. Your best bet is to continue your weekly water changing routine. Every once in a while try for a larger water change. I have gone as far as 75% on a tank. It won't hurt.
The tank size is excellent for the number and variety of fish you have. If they have grown up at the same time, all the better.
There is NOTHING wrong with that Convicts fins.
On a personal note, you should really try and refrin from lashing out at folk who don't immediately jump on your topic. Instead try and shoot off an e-mail to one of the staff or another member.
Given the options, I would take NO answer over the wrong answer anyday. Enjoy the hobby.