B737 DEP FROM OAK RWY 29 EXPERIENCED TCAS RA AT 3000 FT DURING VISUAL SEPARATION APPLICATION WITH OPPOSITE DIRECTION LNDG TFC.

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DEPARTING RWY 29 OAK DURING INITIAL CLBOUT; CHKED IN WITH NORCAL AND WAS GIVEN HDG 300 DEGS MAINTAIN 3000 FT BUT THE ALT WAS GARBLED. ATTEMPTED TO VERIFY 2 TIMES BUT CTLR WAS NOT CLR. LEVELED AT 3000 FT; THEN WAS GIVEN HDG 310 DEGS THEN HDG 030 DEGS; THEN GIVEN 'COMPANY ACFT 12 O'CLOCK POS 3 MI MAINTAINING 4000 FT HAS YOU IN SIGHT.' (FO HEARD COMPANY ACFT DSNDING OUT OF 4000 FT; HAS YOU IN SIGHT.)TCAS TA: MONITOR VERT SPD; THEN AS WE SPOTTED COMPANY; THE ANGLE APPEARED WRONG; THEY WERE CLOSING ON US; ASPECT 180 DEGS NOSE-TO-NOSE. TCAS RA: ADJUST VERT SPD; DSND. IT WAS APPARENT THAT IT WOULD BE VERY CLOSE WITHOUT SOME EVASIVE MANEUVER. WE DSNDED SMOOTHLY AWAY AND COMPANY TURNED AWAY AND APPEARED TO CLB. HEARD COMPANY RPTING THEY WERE COMPLYING WITH AN RA. WE EXCEEDED 250 KTS BELOW 10;000 FT. IT TOOK A COUPLE OF SECONDS TO SEE THAT THE ACFT WAS HEADING DIRECTLY FOR THE ARPT AS IF MAKING A VISUAL TO RWY 11. ATC SHOULD HAVE ADVISED US ABOUT THEIR COURSE AND INTENTIONS. SHE LOST CTL OF THE SITUATION. WE WERE WONDERING WHERE THE SUPVR WAS. IT COULD HAVE BEEN VERY BAD.