The black cap over one of the air intakes is correct. Having one intake capped is what makes the silencer work. If you remove the black cap, it will not affect the performance of the skimmer. If you cap both intakes, then you will be choking the skimmer and the skimmer will not work correctly.
The skimmer is rated for a tank (not including sump) of 130 gals with heavy filtration need. The skimmer will not produce constant skimmate if there is nothing to remove from the water. You have a small system with a very light load so the skimmer will not be as consistent as it would be on a larger system. As time goes by and your system matures and your biological load increases, the skimmer will become more consistent.