CRITICAL CONFLICT ON DEP BTWN A B737-300 FLT AND ANOTHER FLT INBOUND TO CLT; NC.

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FIRST DAY OF 3 DAY TRIP WITH CAPT FLYING AND ME ON RADIO. DIDN'T KNOW CAPT AND HAD NOT FLOWN WITH HIM BEFORE. HE SHOWS UP AT ACFT AT DEP TIME; SITS DOWN AND INTRODUCES HIMSELF. I HAD DONE ALL THE PREFLT TASKS FOR DEP. WE PUSH AND TAXI TO RWY 18R IN CLT FOR TKOF ON RWY 18R; HORNET 1 DEP; NALEY TRANSITION. TAXI/TKOF; THE CAPT HAS HIS SPEAKER ON AND NO HEADSET. I WEAR A HEADSET. WITH HIS SPEAKER ON; I HAD TO TURN MY VOLUME DOWN TO HEAR WITHOUT DISCOMFORT. CAPT UNDER-ROTATES ON TKOF AND IS V2 +20 KTS BEFORE MAINS LEAVE RWY. SHALLOW CLB WITH SPDS APCHING FLAP LIMIT SPDS SHORTLY AFTER TKOF. TWR GIVES 200 DEG HDG AND SWITCH TO DEP FREQ AT FLAP RETRACTION ALT. AS I CHK-IN WITH DEP; CAPT RAISES THE FLAPS HIMSELF. DEP IMMEDIATELY GIVES A 250 DEG HDG THAT I READ BACK. CAPT SAYS 'NO; IT WAS 350 DEGS.' I ASKED CTLR AGAIN; AND AGAIN THOUGHT I HEARD 250 DEGS. CAPT SAYS '350;' AND SETS HIS OWN HEADING TO 350 DEGS. HAVING PROBS HEARING WITH THE SPEAKER ON; I THOUGHT I MUST BE INCORRECT THINKING IT WAS 250 DEGS HE WAS SAYING. I THINK I READ BACK 350 AS WE WERE TURNING TO THAT HEADING. SHORTLY THEREAFTER; WE HAD AN RA ON TFC DSNDING INTO CLT. CTLR ASKED ABOUT THE HEADING AS WE LEVELED TO FOLLOW THE RA. CTLR ALSO VECTORED US L TO AVOID TFC. CONTRIBUTING FACTORS: CAPT SHOWING UP LATE; AND NON STANDARD PRACTICES; IE; NO HEADSET; TKOF PROFILE; MANIPULATING OWN FLAPS AND HEADING ON MCP; WEAK DEP RADIO 120.5 AND DIFFICULTY HEARING WITH HEADSET AND SPEAKER ON SIMULTANEOUSLY; CTLR NOT CHALLENGING MY FINAL READBACK OF AN INCORRECT HEADING OF 350 DEGS.