Ok, your tank is new so it is still cycling. Check out "cycle of the tank" webpage on Kokos site. If the tank is uncycled, you can get many problems from ammonia and nitrate buildup that can kill your fish. Basically, your water parameters are in heavy flux at the moment, and bacteria are going a little nuts in you water. I would suggest doing a 20-30% water change daily until the cloudiness disappears and buying some test kits (ammonia, nitrate, nitrite) to monitor your water. Now when you change the water you must make sure that the temps of the old and new water are similar. Also, there is chlorine in your tap water that is harmful to fish. Either you can buy a de-chlorinator from your local pet store or let your water sit out in a bucket (that was not used for cleaning i.e. new) for 24 hrs before adding it for a water change.
As for the brown gunk on your filter. Well, fish poo. The purpose of the filter is to suck up the poo, and uneaten flakes. You will need to rinse the filter pad every so often, and replace the filter pad about once every month.
Don't replace all your water at once or you will destroy the cycle all over again.
Also, I am sure others will tell you... your tank is overstocked. My fantails are 5-6 inches and comets can get longer than a foot. If you keep them in a 10Gal, they will never grow into the beauties they could become. Also, you will have trouble maintaining water quality and be doing water changes more often. I would suggest taking one or both of the comets back to the pet store.
I know this is a lot to take in, I originally had an overstocked 10gal and problems cycling... I think everyone does when they start out
Goodluck.... I am sure others have more advice