NEAR RWY ENTRY AS SF340 PIC TAXIES OVER HOLD SHORT LINE FOR WRONG RWY 32 AT AEX; LA.

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OUR TAXI CLRNC WAS 'TAXI TO RWY 18 ON TXWY A.' THIS INSTRUCTION WAS CONFUSING BECAUSE OF THE NEED TO BACK TAXI ON RWY 18 FROM THE INTXN AT TXWY A. I REPEATED THIS BACK TO THE GND CTLR (WHO WAS IN TRAINING AT THE TIME) AND THE CAPT VERIFIED THIS INFO WITH ME. THE CAPT BEGAN TO TAXI AND I PROCEEDED WITH THE BEFORE-TKOF CHKLIST SO MY ATTN WAS INSIDE THE ACFT. FOR SOME REASON THE CAPT STARTED TO TAXI TOWARD RWY 36 AND I WAS TOO BUSY TO REALIZE THIS; PLUS I WAS NEW IN MY POS AND UNFAMILIAR WITH THE ARPT. THE NEXT THING I REMEMBER IS THE CAPT CALLING 'CLR L' TO WHICH I NEED TO SAY 'CLR R' WHEN XING A RWY WHILE TAXIING. I LOOKED UP; SAW THAT WE WERE XING A HOLD SHORT LINE; LOOKED R AND SAID 'NOT CLR; STOP.' THERE WAS AN ACFT ON SHORT FINAL FOR THE OPPOSITE END OF THE RWY WE WERE XING. OUR ACFT WAS HALFWAY OVER THE HOLD SHORT LINE AND I LOOKED OVER TO THE RWY SIGN AND NOTICED WE WERE AT RWY 36 ON THE WRONG SIDE OF THE ARPT ENTIRELY. THERE WAS THEN SOME CONFUSION WITH THE GND CTLRS ONCE THEY REALIZED WHERE WE WERE. THEY TOLD US TO JUST PULL CLR OF THE RWY AND HOLD SHORT FOR TKOF ON RWY 32. WE DID SO AND TOOK OFF UNEVENTFULLY. DURING THE ENTIRE INCIDENT AN FAA INSPECTOR WAS IN OUR JUMPSEAT AND DID NOTHING TO PREVENT THE INCIDENT. THIS WAS A BIG FACTOR IN THE INCIDENT; FOCUSING OUR ATTN ON THE INSPECTOR. THE ACFT ON SHORT FINAL DID NOT HAVE TO GO AROUND AND THERE WAS NO 'NEAR MISS.' THIS WHOLE SIT COULD HAVE BEEN PREVENTED WITH MORE STRICT REQUIREMENTS FOR FAA INSPECTORS TO HAVE CURRENT CHARTS/ARPT DIAGRAMS OUT AND AVAILABLE DURING FLT DECK OBSERVATION. ALSO; IMPROVEMENTS TO ATC INSTRUCTIONS CAN BE MADE. ALL RWYS THAT MUST BE CROSSED ENRTE TO THE TKOF RWY SHOULD BE MENTIONED IN EVERY TAXI CLRNC. ALSO A REQUIREMENT TO STATE 'YOU ARE NOT CLRED TO CROSS RWY 14/32' COULD BE ADDED TO ANY TAXI CLRNC ISSUED WHEN MORE THAN ONE RWY IS ACTIVE. THE USE OF L TURN/R TURN MIGHT HAVE HELPED AS WELL. A RESTR ON WHEN CHKLISTS CAN BE PERFORMED WOULD HAVE FOCUSED MY ATTN OUTSIDE MORE AS WELL.