“And I see nothing but US Soldiers there.”
They are part of the UN-established peacekeeping force. NATO may lead it, but the forces are not exclusively NATO.
No, KFOR is purely a NATO force. No UN involvement. No bluers.
Yes, it operates (or was supposed to) under the mandate of UNSC 1244, but that’s it.
A parallel civilian UN mission (UNMIK) was established under UNSC 1244, but KFOR is not subordinate to it in any way. Anymore than our troops in Afghanistan were subordinate to a similar UN mission there (UNSC 1378).
UNMIK has by now been reduced to practically nothing, BTW.