AN ACR BAE146 TOOK A CLRNC FOR A COMPANY ACFT WITH SIMILAR CALL SIGN AND ARTCC CTLR DIDN'T CATCH THE MISTAKE. LATER THE CTLR QUESTIONED THE ACFT'S ALT AND VECTORED FOR TFC; BUT TURNED THE BAE146 THE WRONG WAY AND CAUSED A SYS ERROR BTWN THE BAE146 AND AN ACR B737.

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DUE TO SIMILAR CALL SIGNS I READ BACK A CLRNC FOR ACR AXX TO LEAVE OUR CRUISING ALT FL210 FOR 14000 FT NEAR LAGRANGE. OUR CALL SIGN WAS ACR JXX. THE FEMALE CTLR DID NOT CATCH MY MISTAKE AT FIRST BUT THEN ASKED US TO 'SAY ALT' AFTER WE BEGAN A DSCNT. SHE THEN INSTRUCTED US TO 'AMEND ALT; MAINTAIN FL200.' SHE THEN BEGAN TO ISSUE US VECTORS FOR A DELAY INTO ATLANTA. WE WERE FLYING HDG 120 DEGS; THEN INSTRUCTED TO TURN R TO A HDG OF 360 DEGS AND DSND TO 14000 FT. WHEN PASSING THROUGH 17700 FT A MALE CTLR'S VOICE CAME ON INSTRUCTING US TO DSND IMMEDIATELY THROUGH 17000 FT. AT THIS TIME I OBSERVED LIGHTS OF AN APCHING ACFT WHICH APPEARED TO BE NBOUND AND ABOVE US. 2 SECONDS LATER THE TCASII ISSUED A 'CLB; CLB' COMMAND. MY FO INCREASED PWR AND PITCH TO FOLLOW THE TCASII RA. IN MY JUDGEMENT THE TCASII GAVE US BAD GUIDANCE AS I OBSERVED AN ACR Y B737 JET 2 MI TO OUR L 200 FT ABOVE US. PERHAPS THE CLB COMMAND WAS DUE TO THE FACT THAT WE WERE IN A 30 DEG BANK. I DID NOT TAKE THE CTLS AS I COULD SEE THAT WE WOULD PASS WELL W OF THE INTRUDER. UPON ARR I TELEPHONED THE ATC MGR. HE INFORMED ME THAT WE SHOULD HAVE BEEN ISSUED A L TURN BUT DUE TO OPERROR THE FEMALE CTLR GAVE US A 'R' TURN TO 360 DEGS BY MISTAKE. FATIGUE WAS A FACTOR FOR US AS WE HAD FLOWN 7 HRS PLUS AND HAD BEEN ON DUTY 13 HRS. SUPPLEMENTAL INFO FROM ACN 348363: THE CTLR INSTRUCTED US TO 'TURN R HDG THREE SIX ZERO.' THE CAPT AND I BOTH WONDERED ALOUD WHETHER THEY REALLY WANTED US TO TURN THE LONG WAY AROUND; BUT WHEN THE CAPT READ IT BACK AS 'UNDERSTAND R TURN' THE CTLR DIDN'T RESPOND; SO WE TURNED R. SIMULTANEOUS TO OUR TCASII ALERTS WE HEARD THE OTHER CREW XMIT THAT THEY WERE GETTING AN RA AS WELL; LEADING ME TO PRESUME THAT HE WOULD NOW BE DSNDING; WHICH FURTHER ENCOURAGED ME TO GO UP INSTEAD OF DOWN. DURING A SUBSEQUENT PHONE CONVERSATION WITH ZTL THE SUPVR TOLD THE CAPT THAT THEY HAD ALREADY PULLED THEIR TAPES AND DETERMINED THAT THE CTLR HAD BEEN IN ERROR ABOUT THE TURN DIRECTION. I; HOWEVER; WILL BE MUCH MORE LIKELY TO QUESTION ANY FUTURE ATC INSTRUCTION WHICH 'JUST DON'T SOUND RIGHT;' EVEN AFTER THE READBACK; HEARBACK EXCHANGE! SUPPLEMENTAL INFO FROM ACN 348108: AFTER COMPLETING THE TURN TO 25 DEGS AND STARTING THE DSCNT; I NOTICED AN ACFT ON TCASII AT THE 12 O'CLOCK POS AND BELOW OUR ALT. WITHIN SEVERAL SECONDS AN RA WAS DIRECTED BY TCASII AND WE STOPPED OUR DSCNT (THE TCASII SHOWED THE ALT OF THE OTHER ACFT BELOW OURS) AT APPROX 18000 FT. AT THIS TIME I MADE VISUAL CONTACT WITH THE ACFT AS IT TURNED TO THE W. ACFT SHOWED 200 FT BELOW OUR ALT (ON TCASII) AND LATERAL DISTANCE WAS LESS THAN 1 MI; CLOSE ENOUGH TO VISUAL IDENT THE OTHER ACFT. AT THIS POINT WE ADVISED ATC OF THE RA AND THAT WE HAD STOPPED OUR DSCNT. ASKING FOR FURTHER INSTRUCTION WE WERE TOLD TO CONTINUE DSCNT AND INTERCEPT THE 228 DEG RADIAL OFF ATLANTA. REST OF FLT WAS UNEVENTFUL.