That coral you have in your tank is some sort of sea mat or button polyp. Palythoa sp. would be the most likely scientific name for it.
By the look of it, you have 110 watts of power compact lighting...and 40 watts of normal output flourescents. If this is in fact your lighting you could do fine with most soft corals...colt, leathers, mushrooms. Your polyps which you have in your tank should do fine under those lights....I had some in my tank under worse lighting then that and they did great....
As for what else you would need....it all depends on what you want to keep...for soft corals you are fine...if you wanted LPS corals I would suggest adding more power compacts and getting rid of the marine-glo's. OR you could get rid of everything you have and get all VHO lighting. If you want SPS corals, you will need metal halide.
Additives and Supplements, it's completely up to you. calcium, iodine, strontium are required by all corals so adding them would be a good idea. I simply use Seachem Reef Plus. It's got a little bit of everything, i follow directions on bottle. For calcium I use Kent's liquid calcium....I just pour a couple capfulls in when I notice my calcium levels are down.
If you could take a close up shot of the writing in the bulbs it would help you positively identify your lighting....they could be power compacts....or they could be just fancy flourescent lights that walmart sells
hope this helps somewhat...