Bio-balls, Stars, Live Rock - it's all the same - simply surface area for bacteria. Probs with W/D filters is the filterpad - you want to change tha pad often enough (exporting nutrients) so they can't get into the nitrogen cycle. Bio-balls are not a nitrate factory, well ok they are, but they are suposed to be! Ammonia - Nitrite - Nitrate. If you have a bio-load (anything living) you eventually get Nitrates if all is working ok. Nitrates are the least toxic, and they are handled only by a good fuge, or a DSB, or somewhat poorly by water changes.

Your size tank (47g) probably doesn't need a wet dry, the LR and mechanical filtration should be enough - but your skimmer (if that was a skimmer in the pic?) is probably inadequate. I have about 40g of Bioballs in a huge Wet/Dry in my system, and a huge skimmer, and a 60g fuge, and, and ...

Leave the Bio-Balls or take them out, really doesn't matter, just don't leave waste in the mechanical filter without changing once a week or so - important thing is to test for a stable nitrogen cycle. Once stable for 6+ months the system can pretty much be trusted to maintain itself - just watch for signs of instability.

Carbon - I have a huge bag in my sump 24/7 - change it when I remember and have it on hand - probably 30-90 days. Carbon is an insurance policy - it will quickly absorb toxins released from tank inhabitants and scrubs the water for clarity.