I just managed to obtain the magical 2k (yesss) but now there appears a persistent number (mostly 3 to 5) beside my review pane that simply refuses to disappear after getting rid of all the queues? Does it have something to do with the moderator tools? That's just stats, right? nothing on queue there?
That is the global number of available review tasks, for performance reasons this is cached and not personalized, so reviews that are not available for you because you already did them are still counted.
With 2k reputation you unlocked the availability of that counter permanently, before that you simply don't always see it.