AN MD80 CREW ABANDONS THEIR APCH NEAR THE OM AT MMMX AFTER ENCOUNTERING LIGHT TURB AND HVY RAIN WHILE AT THE SAME TIME RECEIVING WINDSHEAR AND GPWS TERRAIN WARNINGS.

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APCHING PLAZA (MW) ON THE APCH TO RWY 5R AT MMMX; WE NOTED AN ISOLATED STORM CELL IN THE VICINITY OF THE FINAL APCH COURSE. WE CONTINUED AS THE RADAR SHOWED ONLY MODERATE INTENSITY AND NO PLT OR ATC RPTS ADVISING OTHERWISE WERE GIVEN. IN THE TURN OVER MW; AT APPROX 9000 FT MSL; WE ENTERED THE EASTERN EDGE OF THE CELL AND ENCOUNTERED HVY RAIN. VERY SHORTLY AFTERWARD; THE RADIO ALTIMETER RAPIDLY DECREASED THROUGH 1000 FT AND WAS FOLLOWED BY A GPWS LIGHT AND 'TERRAIN; PULL UP.' I ANNOUNCED 'ESCAPE' AT THAT TIME; BUT THE CAPT DID NOT HEAR IT DUE TO THE HVY RAIN. I ANNOUNCED IT AGAIN; THE CAPT BEGAN THE ESCAPE MANEUVER AND ALMOST IMMEDIATELY A 'WINDSHEAR' WARNING OCCURRED AND THE CAPT BRIEFLY MOVED THE THROTTLES FULL FORWARD. AS WE NOTIFIED TWR OF THE GAR/WINDSHEAR; WE EXITED THE WX AND WERE VECTORED FOR ANOTHER APCH. DESPITE THE RADAR ALTIMETER FLUCTUATIONS AND GPWS WARNINGS; SINK RATE WAS STABLE AT 800-1000 FPM DOWN AND AIRSPD REMAINED STABLE AT 160 KTS THROUGHOUT THE EVENT. THE LOWEST ALT I RECALL DURING THE EVENT WAS ABOUT 8600 FT. ADDITIONALLY; I NOTED THAT THE 'STALL INDICATOR FAIL' CAUTION LIGHT ILLUMINATED MOMENTARILY DURING THE EVENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: MAINT DETERMINED THERE WERE NO ENG PARAMETERS EXCEEDED. THEY ALSO FOUND NO PROBS WITH THE RADIO ALTIMETER. THEIR ESTIMATE WAS THAT THE INDICATIONS WERE CAUSED BY THE HVY RAIN ENCOUNTERED IN THE TURN TO FINAL. THE TURB WAS NO MORE THAN LIGHT. NO OTHER ACFT ON APCH RPTED ANY PROBS.