ACR SMT FAILED TO FOLLOW TAXI INSTRUCTIONS TWICE AND NEAR RWY TRANSGRESSION.

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ENRTE TO BNA APCH CTL BRIEFED US TO EXPECT RWY 2L FOR LNDG. WE PUT IN A REQUEST FOR RWY 2R (SHORTER RWY) FOR 2 REASONS: TO HELP OUT ATC DURING A HIGH TFC TIME OF DAY AND TO EXPEDITE OUR TAXI TIME FROM THE RWY TO THE RAMP. OUR REQUEST WAS GRANTED. WE LANDED RWY 2R. ON THE LNDG ROLL AFTER THE ACFT WAS SLOWED AND UNDER CTL; TWR INSTRUCTED US TO TAXI TO THE END AND TURN LEFT ON TXWY CHARLIE. ONE OF THE REASONS WE REQUESTED RWY 2R WAS TO TAXI ACROSS THE APCH END OF RWY 31 AT CHARLIE 9 TO LIMA 5 INTO OUR RAMP LOCATED AT CONCOURSE D. THE CAPT TURNED RIGHT AT ECHO 4. AT THIS POINT WE CONTACTED GND AND TOLD THEM WE TURNED OFF AT ECHO 4. OUR TAXI REQUEST TO CROSS RWY 31 AT CHARLIE 9 WAS DENIED. OUR TAXI INSTRUCTION NOW WAS TO TURN LEFT ON TXWY CHARLIE; CROSS '20L' AND TURN RIGHT ON BRAVO AND HOLD SHORT OF RWY 31. WE TAXIED DOWN TXWY CHARLIE. WE BOTH SAW TXWY BRAVO AND PROCEEDED PAST BRAVO AND WERE ON OUR WAY TO XING AN ACTIVE RWY (2L) WHEN GND IMMEDIATELY BURST ONTO THE RADIO AND TOLD US TO STOP AND HOLD OUR POS. THE PROB IS 2-FOLD. WE AS A CREW WERE NOT TOO FAMILIAR WITH THE ARPT LAYOUT AND WE TURNED OFF THE RWY AT ECHO 4 WHEN WE WERE TOLD TO TURN LEFT ON CHARLIE AT THE END OF RWY 2R. THIS IS OUR FAULT. THE CONFUSION IS THAT WE WERE AT ECHO 4; WERE TOLD TO TURN L ON TXWY CHARLIE AND CROSS RWY 20L. WE HAD JUST LANDED RWY 2R. WE BOTH THOUGHT WE WERE TO CROSS RWY 2L AS WE HAD EVERY INTENTION TO DO EVEN WHEN WE SAW TXWY BRAVO PASS. WE FEEL OUR TAXI INSTRUCTIONS WERE MUCH A CONTRIBUTING FACTOR. WHAT I CANNOT FIGURE OUT IS WHY WE WERE TOLD TO CROSS '20L.' RWY 2R WAS THE ACTIVE RWY. WHY WERE WE NOT TOLD TO CROSS RWY 2R? THIS WOULD HAVE ALLEVIATED THE PROB (ALONG WITH THE FACT WE DIDN'T DO WHAT WE WERE TOLD BY TWR.' THERE WOULD NOT HAVE BEEN ANY CONFUSION WITH THE PARALLEL RWYS. THIS IS NOT THE FIRST TIME I HAVE RUN INTO THIS PROB OF BEING CLRED ACROSS INACTIVE RWYS WHICH ARE ACTIVE. IF AN ACFT IS TO CROSS AN ACTIVE RWY IT SHOULD BE STATED AS TO THE ACTIVE RWY WHICH IS ACTIVE; DESPITE WHERE YOUR POS IS ON THE ARPT.