A CPR FLC FLYING A CL601 AT DFW RPTS A TCASII RA WHILE MANEUVERING THEIR ACFT FOR A VISUAL APCH TO LAND.

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APCH CTL HAD US ON APPROX A 240 DEG HDG AND APPROX 6000 FT; AND WE REQUESTED RWY 18L/R; BUT NO RWY WAS ASSIGNED. WE WERE WITHIN 20 MI OF DFW ARPT. FINALLY; APCH CTL CLRED US DOWN TO APPROX 3000 FT AND ASKED IF WE HAD THE ARPT IN SIGHT. CAPT RESPONDED YES AND WE WERE CLRED FOR VISUAL APCH TO RWY 17L. THEN AFTER ABOUT 15 SECONDS ATC SAID TURN TO APPROX 270 DEG HDG AND TURN FINAL OUTSIDE OF A FIX THAT I WAS NOT FAMILIAR WITH AND STILL CLRED FOR THE VISUAL APCH TO RWY 17L. CAPT PROCEEDED TO PUT THE FIX IN THE FMS; AND SET UP A COURSE INTERCEPT OFF OF THE FIX. AT THIS TIME I WAS HAND FLYING THE ACFT AND LOOKING OUT THE WINDOW TRYING TO VISUALLY LOCATE THE ARPT/RWY 17L SINCE I HAD NEVER IDENTED THE ARPT/RWY EVEN THOUGH THE CAPT HAD ACCEPTED A VISUAL APCH. ALSO; WHILE I WAS TRYING TO LOCATE THE ARPT/RWY 17L; I WAS MONITORING SEVERAL OTHER ACFT AROUND US. THEN WE RECEIVED A TCASII RA; WHILE I WAS DSNDING ON A VISUAL APCH ON AN ACFT WHICH I WAS ALREADY MONITORING. THE TCASII RA WAS INFORMING US TO DSND WHICH I WAS ALREADY DOING. THE CAPT TOOK CTL OF THE ACFT AND CONTINUED TO DSND AS WELL AS TURNING THE ACFT TO THE L UNTIL THE RA WAS RESOLVED. CAPT THEN RETURNED CTL OF THE ACFT BACK TO ME AND ATC CALLED US AND SAID THAT WE WERE LINING UP FOR THE WRONG RWY. THE CAPT APOLOGIZED AND INFORMED ATC THAT WE WERE ALREADY TURNING BACK TO LINE UP FOR RWY 17L. AFTER; THE RA WAS RESOLVED I WAS ABLE TO VISUALLY IDENT THE ARPT/RWY 17L. WE PROCEEDED IN FOR A LNDG ON RWY 17L.