Start by checking the row of LED-s on the Numark. They show the output level from the Numark. If they are not blinking, the Numark does not send any signal. If not, where is your signal supposed to come from? You need to check the settings in the Numark or the input source.
Turn up the levels on the Numark so that at least half of the red LED-s light up.
This isn't going to be possible. The power-adapter unit that sits between the connector and the mic is where the power comes from. It is not going to be possible to bypass this. Bear in mind that the TRRS connector is wired primarily to provide microphone input to a smartphone. The "Left and Right" (TR) is likely not connected to anything at all.