AN ACR MLG HAD TROUBLE WITH MULTIPLE LANGUAGES AND UNDERSTANDING CTLR AT SJD.

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INBOUND TO THE LOS CABOS ARPT; TWR CLRED US FOR A VOR DME APCH TO RWY 16. OVER THE VOR; WE TURNED TO A HDG TO INTERCEPT THE OUTBOUND COURSE. I RPTED ARPT IN SIGHT FOR A VISUAL TO THE TWR AND WAS CLRED FOR A VISUAL APCH WITH THE LAST PART OF HIS XMISSION NOT UNDERSTANDABLE TO US. I ACKNOWLEDGED CLRED TO LAND TO THE TWR WHILE CONTINUING THE DOWNWIND LEG TO LOSE ALT. AT THAT TIME; TWR STARTED TALKING TO ANOTHER AIRPLANE IN SPANISH. WE WERE NEVER INFORMED OF TFC IN THE AREA. I ASKED TWR TO SAY AGAIN HIS LAST XMISSION; AND AGAIN WE COULDN'T UNDERSTAND THE LAST PART OF HIS XMISSION. WE TURNED BASE LEG AND I ASKED TWR IF WE WERE CLRED TO LAND AND TWR SAID; 'HOW DO YOU READ ME?' THE FO THEN ASKED FOR LNDG CLRNC AND TWR SAID; 'NEGATIVE.' I WAS CONFUSED AT THIS TIME BECAUSE THE RWY WAS CLR. AGAIN; TWR STARTED TALKING TO ANOTHER AIRPLANE IN SPANISH. TWR THEN CLRED US TO LAND AND STATED; 'I HAVE THE RPT.' I THEN SAID TO THE FO 'I THINK THAT TWR WANTED US TO EXTEND OUR DOWNWIND LEG.' WE LANDED; MADE A 180 DEG TURN AT THE END OF THE RWY AND STARTED TAXIING TO THE RAMP WHEN TWR INSTRUCTED US TO EXPEDITE TAXI WITH NO REASON GIVEN. BEFORE I TURNED OFF THE RWY; I COULD SEE A SINGLE ENG CESSNA ATTEMPTING TO LAND ON RWY 16. TWR THEN STATED; 'SEE WHAT YOU'VE DONE; THAT'S THE SECOND GAR FOR THAT AIRPLANE.' I CALLED THE TWR FROM OP TO CLARIFY WHAT WAS GOING ON. THE CTLR DIDN'T WANT TO LISTEN TO ME. HE SAID WE NEVER ACKNOWLEDGED HIS XMISSIONS AND THAT HE HAD IT ON THE TAPES. HE ALSO STATED THAT I'M REQUIRED TO UNDERSTAND ALL OF HIS XMISSIONS ACCORDING TO THE REGS. I FELT FURTHER CONVERSATION WITH HIM WOULDN'T RESOLVE THIS ISSUE.