B757 FLC HAS QUESTION REGARDING LNDG CLRNC. AFTER LNDG; TOLD ARPT CLOSED.

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DSNDING INTO QUITO ARPT AT XA45 LCL VMC WITH SOME SCATTERED TO BROKEN CLOUDS. CLRED FOR ILS APCH AND LNDG ON RWY 35 AT UIO. WE SAW WHAT LOOKED LIKE SOME SCATTERED PATCHY GND FOG. THE 30 MIN OLD WX WAS CLR SKY; 10 NM VISIBILITY. ON DOWNWIND THE APCH CTLR ISSUED SOME INFO ABOUT THE WX; BUT WE DID NOT UNDERSTAND IT. THE ARPT WAS IN SIGHT DURING THE DOWNWIND LEG. AFTER WE WERE ESTABLISHED ON THE ILS LOC AND GS WE ENTERED THE CLOUDS AT THE SAME TIME THAT THE CTLR GAVE US SOME MORE WX INFO. WE THOUGHT HE RPTED 2 MI VISIBILITY. THE REQUIRED VISIBILITY TO BEGIN THE APCH IS 4 NM; BUT WE WERE ALREADY ESTABLISHED INSIDE THE FINAL APCH FIX. WE SAW THE RWY ABOUT 150-200 FT ABOVE THE MDA. ATC DID NOT RESPOND WHEN WE ASKED HIM TO VERIFY THAT WE WERE CLRED TO LAND. WE THOUGHT WE WERE PREVIOUSLY CLRED TO LAND; SO WE CONTINUED AND LANDED. WE ENTERED A FOG BANK DURING ROLLOUT. WE WERE THEN INFORMED THAT THE FIELD WAS CLOSED. WE BELIEVE WE COMPLIED WITH OUR CLRNC BUT AFTER WE LANDED THERE WAS SOME QUESTION AS TO WHETHER THE FIELD WAS OFFICIALLY CLOSED BEFORE WE LANDED OR AFTER. LANGUAGE DIFFERENCES CONTRIBUTED TO THE SIT.