Its difficult to understand what your filter problems are. Would help if you could give the brand name and model of filters.
It sounds like the second filter is a power head. If it is then you don't need the air tube. And if it is a power head then yes it should run 24-7 but without the air tube.
Have you added salt to the water? Can't add salt water fish till salt is in and tank has cycled.
I would take out the crab and fish and cycle the tank.
Use the shrimp method described in article. Basically you get a raw shrimp from grocery store and drop in tank and let it rot. This will establish the bacteria you need to breakdown waste products. Fresh water bacteria and salt water bacteria are different so have tank run freshwater will not prepare it for salt.
You wouldn't need special lights for fish or live rock, NO
salt water fluorescents (not plant or freshwater bulbs) running about 12 hrs is sufficient. Corals, anemones and clams need more light.