You might get a better response if this were in General marine rather than Do-It Yourself.
External filters aren't usually used in SW systems since the media can act as a trap for detritus, which contributes to high nitrates. If you want to run it with no media, just for increased circulation, no problem. With the 2 powerheads, I probably would run it, just to help avoid dead spots. Increased circulation would probably reduce the brown algae on the sand. This isn't actually algae--they're diatoms. Very common in new tanks. It will clear up on it's own.
The lighting info isn't very useful-what type? NO, VHO, MH, PC? Wattage ratings are needed to determine if you're providing enough light to support photosynthetic creatures or not.
Sponges sold for use in the kitchen tend to come with anti-fungal treatments--not good for your tank. Never use a sponge which has been used with soap--very bad. I prefer scrapers--kent makes some good ones. Just easier, doesn't involve as much elbow grease.
I tend to avoid using chemical filtration (products like ammo-lock, ect) since they can cause problems for the biological filtration. Test kits are great, as long as they are used regularly and reliably.
A skimmer might be needed--it really depends on what you're got in the tank. For a reef system I wouldn't run one without it. For a FO, or a FOWLR, guess it would depend on what the bio-load was like, and the maintenance routine.