A320 CREW LNDG LAS ON RWY 4R INITIATES A GAR AS A RESULT OF NOT BEING STABILIZED BECAUSE OF A STRONG TAILWIND.

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GAR EXECUTED AFTER VISUAL APCH TO RWY 7R; WHEN NOT STABILIZED BY 500 FT AGL DUE TO VERY STRONG TAILWIND (40 KTS AT 4000 FT AGL; DECREASING TO 14 KTS SHORT FINAL) WITH SURFACE WINDS AT 120 DEGS/10 KTS. DURING INITIAL PHASE OF GAR; WHEN STILL ABOVE CONCRETE RECEIVED 'TFC' TCASII ADVISORY. UPON CLBOUT; ATC QUERIED; 'ACR X; DO YOU NEED ASSISTANCE?' THE CAPT RESPONDED; 'NEGATIVE.' WE RECEIVED A SECOND 'TFC' TCASII ADVISORY. ATC AGAIN QUERIED; 'ACR X; DO YOU NEED ASSISTANCE?' THE CAPT SAID; 'ACR X; NEGATIVE. WE HAD A WIND SHIFT ON SHORT FINAL AND WERE NOT STABILIZED; AND THEREFORE WENT AROUND.' WE WERE GIVEN A TURN TO 090 DEG HDG. ATC AGAIN ASKED; 'ACR X DO YOU NEED ASSISTANCE?' THIS WAS VERY DISTRACTING; AND BOTH PLTS LOOKED DOWN TO VERIFY THAT THE CAPT WAS IN FACT XMITTING ON VHF #1. THE CAPT SAID; 'FOR THE 3RD TIME; NO. ACR X DOES NOT NEED ASSISTANCE.' AT THAT SAME TIME WE RECEIVED A TCASII RA FOR 'MONITOR VERT SPD' REQUIRING APPROX A 3000+ FPM CLB. AFTER THE CAPT'S LAST XMISSION WE WERE TOLD THAT THERE WAS ALSO AN ACR Y ON FREQ. THE CAPT HAD BEEN LOOKING FOR TFC DURING ENTIRE GAR PROC AND FINALLY SAW AN ACR Y APPROX 100 YDS OFF OUR L WING. WE RECEIVED THE 'CLR OF CONFLICT' ANNOUNCEMENT SHORTLY. AFTER ANALYZING WHAT HAD HAPPENED; WE FELT LIKE IT WAS THE 'PERFECT STORM' FOR A MUCH MORE SERIOUS SIT. DURING OUR GAR AN ACR Y WAS TAKING OFF ON RWY 7L. ATC WAS SURPRISED AT OUR GAR; ALTHOUGH LESS SO WHEN THE 2 ACFT WHO LANDED BEHIND US RPTED AN AIRSPD LOSS OF 10 KTS AT 100 FT ON SHORT FINAL FOR RWY 7R. INITIALLY; BOTH ACFT WERE MAINTAINING RWY HDG. WE BELIEVE THAT WHEN WE WERE ASSIGNED THE 090 DEG HDG THAT ACR Y ALSO TURNED TO THE 090 DEG HDG. WE DO NOT BELIEVE THAT THE ACR Y ACFT SAW US; AT LEAST UNTIL THE TCASII RA. IT IS LIKELY THAT THEY WERE UNAWARE; AS WE WERE; THAT THERE WAS ANOTHER 'ACR X' CALL SIGN ON FREQ. ALTHOUGH ATC NEVER SAID ANYTHING ABOUT A LOSS OF SEPARATION; WE BELIEVE THAT WE WERE DEFINITELY TOO CLOSE TO THE ACR Y. WE RETURNED FOR A LNDG ON RWY 7R THAT WAS UNEVENTFUL.