Carbon has only a few uses - it removes medication after a treatment has finished, it removes the brown colour that leaches out of bogwood, and it removes peculiar smells.
The reason it is in new filters is historical. Going back several decades, the nitrogen cycle was not known to fish keepers. They rarely did water changes as they considered them dangerous to their fish, and the water slowly turned yellow because of all the things secreted by the fish and plants, if they had any. They didn't like this yellow colour, so they had filters to removes it. My parents had a book dating back to the 1960s on how do do repairs, and there was a section on fish (how to repair a leaky tank with putty; how to change the diaphragm in an air pump; how to repair a faulty heater thermostat) and it showed a cross secton through a filter. It was just a box containing carbon granules with a layer of filter wool on top, and water was sucked through by an air pump.
People resist change. Even after the nitrogen cycle became understood, and filters evolved through undergravel ones to today's filters, fishkeepers still wanted their carbon. So manufacturers included it in the box. And new fishkeepers found the carbon in the package so assumed it was necessary.
If you mean Interpet Filter Aid, I never found that worked very well. What might help is to replace the carbon sponge with a superfine pad rather than another plain sponge. They will catch smaller particles than a plain sponge but will be a home to the filter bacteria.
The water can become cloudy after a water change as cleaning the gravel (assuming you did that) can throw up light debris into the water column. The filter should suck it up quite quickly, especially if you had a fine pad (or even a layer of filter wool) inside the filter. And this debris is then washed out when you clean the filter by squeezing the sponges/pads in water that you take out during a water change.