FAULTY ALT ENCODING FOR THE #2 TRANSPONDER ON A CHARTER ACFT LEADS TO A TCAS RA EVENT.

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AFTER TKOF FROM KJVY RWY 18; APCH CTL GAVE US A TURN TO 030 DEGS. THE CTLR THEN GAVE US A TURN TO 190 DEGS BECAUSE HE INITIALLY THOUGHT WE WERE DEPARTING RWY 36. WE WERE THEN CLRED TO CLIMB TO 6000 FT; AND DIRECT TO IIU. I ASKED FOR DIRECT KGYH; AND THE CTLR CLRED US TO PROCEED. WHILE PASSING ABOUT 5800 FT; THE CTLR TOLD US TO CHECK OUR ALT; WE WERE ABOVE 6000 FT ON THE RADAR. I RESPONDED THAT WE WERE NOT AT 6000 FT BUT AT 5800 FT CLIMBING. HE TOLD ME TO DESCEND; AND THAT I WAS CONFLICTING WITH AN ACR ACFT Y OVERHEAD. THE ACFT Y TOOK EVASIVE ACTION ACCORDING TO THEIR TCAS; I ASSUMED CTL OF THE ACFT AND PROCEEDED TO DESCEND TO ABOUT 5600 FT. I THEN ASKED FOR A LCL ALTIMETER; AND OUR ALTIMETER CHECKED TO BE SET TO THAT SETTING. I ALSO DECIDED TO SWITCH TO TRANSPONDER #1; AND VERIFIED THE ALT WITH THE CLTR. THE CLTR THEN TOLD ME I NEEDED TO CONTACT THEM ON THE END OF THE FLT. THE REST OF THE FLT WENT NORMAL. I FEEL THAT THE FAULTY #2 TRANSPONDER ALT REPORT WAS THE CAUSE OF THE TCAS ALERT. ALSO; UPON TKOF; THE CTLR THOUGHT WE WERE GOING TO DEPART RWY 36; INSTEAD OF THE RWY 18 WE USED. USUALLY AT KJVY; THE SOP IS TO HOLD FOR RELEASE; AND ADVISE RWY OF DEP. THIS TIME; THE CTLR ASKED DURING GETTING THE CLRNC; AND MY FIRST OFFICER HAD INITIALLY SAID WE WOULD DEPART RWY 36. BEFORE TKOF WE ASKED FOR IFR RELEASE AND TOLD THE CTLR WE WERE 'NUMBER ONE' FOR RWY 18. THE CLTR NEITHER REJECTED OR ACKNOWLEDGED THIS. OTHER CONTRIBUTING FACTORS WERE THE CTLR NOT CONFIRMING OUR ALT ON INITIAL CONTACT AND THE CTLR DID NOT OFFER THE LCL ALTIMETER SETTING. THE TRANSPONDER #2; LATER ON IN THE CONTINUATION OF THE FLT WAS CONFIRMED WITH CENTER TO BE OFF SOME 800 FT.