A319 FLT CREW; WHILE ATTEMPTING A NON PRECISION APCH TO DCA; EXECUTES A MISSED APCH AND DEVIATES FROM ASSIGNED HEADING CAUSING A TCASII RA EVENT AND A EGPWS WARNING.

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ON APCH INTO DCA; I WAS FLYING (CAPT). WE WERE CLRED FOR THE LDA APCH TO RWY 19 AND WERE ON AUTOPLT. ACFT FLEW THROUGH COURSE AS WE WERE DSNDING TO 3000 FT MSL. IT MADE A TURN BACK TO INTERCEPT COURSE. I DECIDED WE WERE TOO HIGH AND ASKED THE FO TO GET US VECTORS. WE WERE GIVEN A HEADING OF 270 DEGS MAINTAIN 3000 FT MSL. STARTED TURN FROM APPROX 170 DEGS AND 2500 FT MSL. THE ACFT DID NOT RESPOND CORRECTLY; SO I FELT IT NECESSARY TO DISCONNECT THE AUTOPLT AND MANUALLY MAKE TURN AND CLB. FORGETTING THE ACFT WAS IN THE APCH MODE; I DID NOT TURN OFF FLT DIRECTORS OR APCH BUTTON AND DID NOT GO TO TOGA. CONSEQUENTLY; THE ACFT STARTED SLOWING DOWN. I TURNED OFF THRUST LEVERS FOR MANUAL CTL. WITH THESE DISTRS I TURNED THROUGH 270 DEG HDG TO APPROX 320 DEGS; ATC ISSUED INSTRUCTIONS TO TURN BACK. AT THE SAME TIME WE WERE CLEANING THE ACFT UP; SO NO ACFT PARAMETERS WERE EXCEEDED. WE THEN RECEIVED A TCASII WARNING TO DSND; WHICH I DID RAPIDLY. AT THIS POINT THE FLT DIRECTORS WERE OFF. THEN A GPWS TERRAIN WARNING OCCURRED; ONCE. I LEVELED OFF IMMEDIATELY; IT STOPPED AND WE CLBED BACK TO 2000 FT MSL. I DO NOT BELIEVE WE WERE THAT LOW; APPROX 1800 FT MSL. THE TCASII WAS GONE. FLEW UNEVENTFUL APCH TO LNDG. ATC INFORMED ME ON THE GND WE PASSED WITHIN 1 1/2 MI AND 400 FT OF ANOTHER ACFT. APPARENTLY I MUST HAVE BEEN MORE FATIGUED THAN I REALIZED; AS I WOULD HAVE NEVER MADE THESE ERRORS IN JUDGEMENT.