>why do saltwater tanks need protein skimmers while fresh one do not?
Because skimmers don't function at neutral or low pH, as are present in most freshwater tanks.
>do carbon take out salt in the water?
No. It is commonly used in saltwater tanks.
>how to maintain salt levels?
Once you have established the correct salinity when the tank is set up, water loss from evaporation is replaced by adding freshwater. Salinity should be checked regularly, especially when you are starting out.
Please buy or borrow and read Fenner's Conscientious Marine Aquarist. It will answer these, and many more questions that you might not have considered, and I guarantee will save you a lot of heartache.