Can my DJ performances be recorded?

Yes.
But, the sound input from the Mic input terminal of this unit can not be recorded.
Operate rekordbox as described below.
1. Click the [REC] icon at the top left of the screen to open the recording panel of rekordbox.
2. Click the [REC] button in the recording panel to start recording.
To end recording, click the [REC] button again.
When recording completes, a file is saved automatically.

For details, refer to the "Recording" section in the "Rekordbox Software Manual." Download the "Rekordbox Software Manual" from the rekordbox website.
http://rekordbox.com