A B767 PIC RPT ON RWY CHANGES IN LAX AND THE CONFUSION IN APCH CLRNCS THAT CREATED A POTENTIAL CONFLICT DURING A CHANGED APCH TO RWY 24R AT LAX; CA.

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JUST OUTSIDE OF CIVET INTXN; APCH CHANGED FLT TO MITTS 2 ARR AND RWY 24R. WE HAD PREVIOUSLY BEEN CLRED ON CIVET APCH TO RWY 25L. WE WERE FLYING ON AUTOPLT AND TOLD OF TFC ON APCH TO RWY 25L. ACFT WAS IN SIGHT AT ALL TIMES. I TOOK ACFT OFF AUTOPLT TO HAND FLY THE APCH DUE TO DIFFICULTY IN IDENTING THE APPROPRIATE FIXES (ILS/DME) AND WE TRANSITIONED TO RAW DATA. WE RECEIVED A 15 DEG TURN TO THE R FROM APCH DUE TO CONFLICTING TFC AND JUST AT THIS POINT RECEIVED AN RA ON TCASII. THIS WAS FOLLOWED (CLB RA) AND THE R TURN AS ADVISED PROVIDED ADEQUATE SEPARATION FROM ACFT AHEAD AND TO OUR L. THE LATE CHANGE OF THE ARR PROC WAS PARTIALLY RESPONSIBLE FOR THE CONFUSION; BUT I SHOULD HAVE ANTICIPATED A CHANGE AND BEEN USING RAW DATA AS A BACK-UP MUCH EARLIER. THERE WAS ALSO SOME CONFUSION AS TO OUR DSCNT CLRNC. WE WERE NOT SURE IF WE WERE CLRED TO DSND VIA THE ARR. IN ADDITION; WE WERE CAUGHT HIGH AND FAST; ESPECIALLY BTWN SNRKL AND JONZZ. I WILL ANTICIPATE THESE CHANGES AND HAVE RAW DATA AVAILABLE FOR THESE APCHS NEXT TIME RATHER THAN RELYING ON FMS DATA AND AUTOPLT FOR THESE APCHS FROM NOW ON.