DC9 FLC VECTORED THROUGH LOC; MAKES MISSED APCH; MISHEARS VECTOR HDG.

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ON EXECUTING A MISSED APCH AT MDW ARPT; I UNDERSTOOD THE WRONG HDG FROM THE CTLR; 320 DEGS VICE 220 DEGS; WHICH I READ BACK TO THE PNF. IN MY TURN TO 320 DEGS THE FO QUERIED APCH CTL ON ASSIGNED HDG AS WE WERE PASSING APPROX 270/280 DEGS IN TURN AT 2600 FT MSL. CTLR GAVE US AN IMMEDIATE TURN AND CLB FOR TFC AVOIDANCE. PART OF THE PROB WAS A RESULT OF A VERY HURRIED APCH; WHERE WE WERE GIVEN A VECTOR THROUGH THE LOC AND THEN REQUIRED APPROX 50 DEG TURN BACK TO LOC TO ATTEMPT CAPTURE. WE CROSSED THE MARKER AT 2600 FT AND FAILED TO CAPTURE LOC UNTIL MOMENTS LATER. ATTEMPTED TO MISS THE APCH AT THAT TIME WITH APCH CTL WHO DIRECTED US TO TWR BECAUSE OF DEPARTING TFC. I DID ATTEMPT TO CATCH UP TO GS BUT WAS UNABLE; AND SUBSEQUENTLY MISSED APCH. THERE WAS A GREAT DEAL OF CONGESTION ON APCH/DEP AND WE WERE QUITE HURRIED IN COCKPIT ALL OF WHICH CONTRIBUTED TO MISUNDERSTANDING OF HDG ASSIGNED BY DEP/APCH CTL; ALL OF WHICH WOULD HAVE BEEN ALLEVIATED BY EITHER BETTER HANDLING IN THE VECTORING TO APCH OR IN FLYING PUBLISHED MISSED APCH PROCS. ADDITIONAL TO ATC PROBS WE ENCOUNTERED ON OUR MISSED APCH; THE FLT DIRECTOR COMMAND BARS ONLY COMMANDED A 5 DEG NOSE UP ATTITUDE WHICH ALLOWED A MOMENTARY SINK RATE TO OCCUR; AS I DISENGAGED FLT DIRECTOR AND PROCEEDED ON RAW DATA. FO CHANGED HIS ATTN SPAN FROM ATC TO PROVIDE ME WITH ASSISTANCE ON SINK RATE AND ALT CALLOUTS. THIS ALSO CONTRIBUTED TO OUR MISSING ASSIGNED HDG. GND TEST OF FLT DIRECTOR AT ENRTE DEST STOP INDICATED THAT FLT DIRECTOR INDEED HAD MALFUNCTIONED IN GAR MODE AND WAS ONLY COMMANDING APPROX 1/2 OF REQUIRED INPUT.