CHK AIRMEN AND REQUALIAFYING A320 CAPT ENCOUNTER MULTIPLE RWY CHANGES AND QUESTIONABLE ATC HANDLING ON APCH TO MMMX.

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HANDS FULL APPROACH/GO AROUND DUE TO RWY CHANGE. ON DESCENT 1 HOUR OUT; WE BRIEFED VOR RWY 5R APPROACH; NOTING THAT THERE WAS A NOTAM FOR RWY 5R 109.1 FREQUENCY UNSERVICEABLE. SINCE THIS WAS A REQUALIFICATION TO NEW CAPT AN EXTENSIVE BRIEF WAS ACCOMPLISHED WITH ALL OTHER RWY REASSIGNMENTS AND APPROACH NAV PROCEDURES. EARLIER REPORTS SHOWED WINDS CALM LANDING 5R WITH CEILING OF 2000 FEET. AS WE APPROACHED PTJ VOR WINDS WERE NOW 190/08 AND ATC REROUTED US FOR RWY 23L APPROACH. NO INDICATION OF TYPE OF APPROACH WAS GIVEN AND SO WE EXPECTED RWY 23L; SINCE THE NOTAMS DID NOT SPECIFICALLY STATE RWY 23L FREQUENCY WAS UNSERVICEABLE. WE WERE IN IMC CONDITIONS WITH MODERATE RAIN (YELLOW ECHOES) THE ENTIRE ARRIVAL AND SOME TURBULENCE. WE WERE GIVEN A HEADING TO INTERCEPT RWY 23L AND CLEARED FOR RWY 23L VOR. AS WE BEGAN TO DESCEND TO THE ASSIGNED ALTITUDE OF 9000 FT I BEGAN TO SELECT THE VOR RWY 23L APCH ON THE FMGC. THE STUDENT CAPTAIN HAD JUST DISCONNECTED THE AUTOPLT; WHICH CAUGHT ME BY SURPRISE AS I THOUGHT IT WOULD HAVE BEEN BEST TO HAVE THE AUTOPLT ON. ALL WAS GOING NORMAL AND THEN SUDDENLY ATC ISSUES CLIMB TO 11;000 FT AND DIRECT TO SMO FOR RWY CHANGE TO 5'S. THE CAPTAIN IMMEDIATELY GOES TO TOGA BUT DOES NOT PITCH TO 15 DEGREES. I SCRAMBLED TO INSERT SMO IN THE BOX BUT TWO CHOICES COME UP SO I TAKE A MOMENT TO CONFIRM THE CORRECT VOR. THE GO AROUND WAS SLOPPY AND HAND FLOWN. ATC WAS ISSUING MANY HEADINGS TO INTERCEPT THE 160 DEG R FROM SMO AND IN THE PROCESS OF REPLYING I MOVED THE SIDESTICK CAUSING A BRIEF 'DUAL INPUT' ALERT. I IMMEDIATELY RELEASED THE SIDESTICK AND WAS MORE CAREFUL WHEN PRESSING THE PUSH TO TALK BUTTON. WE GOT LEVEL AT 11000 FT AND WERE NOW ON HEADING TO INTERCEPT THE 160 DEG R FROM SMO OUTBOUND. AT THIS POINT I COMMANDED THE CAPTAIN TO TURN THE AUTOPLT ON TO ASSIST US ON THE HEAVY WORKLOAD; AND HE DID. PRIOR TO INTERCEPTING THE RADIAL; ATC GAVE US ANOTHER HEADING AND A DESCENT TO 9700 FEET. THEN ANOTHER HEADING OF ABOUT 210 TO INTERCEPT THE MEX 232 INBOUND. THEN WE WERE GIVEN A FINAL INTERCEPT AND 8800 FT TO INTERCEPT THE RADIAL AND CLEARED FOR THE RWY 5R VOR APPROACH. JUST AS I WAS SETTING UP THE BOX WE BROKE INTO THE CLEAR AND WE SAW THE AIRPORT AS WE WERE ON A LEFT BASE AND TOLD THE CAPTAIN THAT WE COULD DO A VISUAL; AND WE DID WITH NO FURTHER EVENTS. CONCERN -- MEXICO APCH DECISION TO ABORT OUR APPROACH WITH IMMEDIATE COMMANDS AND COMPLEX INSTRUCTIONS WAS DAUNTING. WE WENT AROUND AND LANDED IN LESS THAN 5 MINUTES. WITH MOUNTAINS AND WX WE FELT TRAPPED TO COMPLY UNLESS WE WERE VECTORED AWAY FROM ALL HAZARDS. PILOT -- CAPTAIN DISCONNECTED THE AUTOPLT MISUNDERSTANDING OUR PREVIOUS DISCUSSION AND SHOULD HAVE KEPT THE AUTOPLT ON TO ASSIST WITH APCH AND GO AROUND. EXECUTION OF GO AROUND WAS SLOPPY AND THUS CREATED FURTHER WORKLOAD. NOT TURNING AUTOPLT ON IMMEDIATELY TO ASSIST ALSO CONTRIBUTED TO WORKLOAD.