Question

When did Serbia and Montenegro split? And what, exactly, is Kosovo? Thank you.

Answer 1

Serbia and Montenegro spit definitely in 2006, although the country was before called "Serbia and Montenegro", and there were clear boundaries between the territories. 

Kosovo is, depending on the point of view, a independent country in the Balkans, with an Albanian population, or a part of Serbia.

The thing is that Serbia has no de facto power over Kosovo, and Kosovo is de facto independent, but on the international stage not every country recognizes Kosovo as an independent country.