@Trancer > The CDJ350 IS compatible with Traktor (and other DJ titles, including VirtualDJ, Ableton, etc), you simply need to load a TSI file for it instead of using the Setup Wizard. See this page for more information and the TSI file download.
As for the "chirping", that's the original cueing method -- pre-vinyl-mode days. It's simply a 1-frame loop allowing you to find the place you want to cue the audio. If you don't want to hear that, press the VINYL MODE button.