Can the Pioneer CDJ-2000 player play music purchased from iTunes (both DRM protected, and without DRM)?

No, Apple uses DRM copy protection on all items purchased through the iTunes Store in order to prevent you from playing the songs anywhere but on Apple device. Pioneer CDJ-2000 player is not an iTunes supported device. If your Pioneer CDJ-2000 player is the primary device you plan to use for playing back songs on the go, I would suggest removing DRM from iTunes music files, 2 ways as follows:

1.Buy songs on iTunes. just Insert a blank CD. (You'd better use a rewrite CD which can be used circularly and use some software like Nero to wipe off the music files you have processed.)

Note: You need to change iTunes settings in "Edit"->" Preferences" before burn and import.

2. Another option would be to purchase software that automatically converts your iTunes purchases to MP3. An app called DRM Converter does this quickly, it support batch conversion that can convert protected itunes Music Video files to Pioneer CDJ-2000 player mp3 for playback without quality loss. you may check it here:

http://www.drm-removal-tool.com/drm-converter.html