A DHC8 CREW HAD AN NMAC; THEN LTSS WITH 2 DIFFERENT ACFT WHILE IMC.

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WHILE ON RADAR VECTORS FOR AN ILS APCH TO RWY 10L AT CMH; WE HAD 2 NEAR MISSES OCCUR WITHIN A FEW SECONDS OF EACH OTHER. EVENTS DEVELOPED QUICKLY; SO THE SEQUENCE MAY BE IN ERROR. PARALLEL APCHS TO RWYS 10L AND 10R WERE IN USE IN CMH. WE HAD BEEN ASSIGNED RWY 10L. ALL NAVAIDS HAD BEEN TUNED AND IDENTED AND AN APCH BRIEFING COMPLETED. THE TCASII HAD ALSO BEEN TESTED EARLIER AND WAS OPERATING NORMALLY IN TA/RA. THE FO AS THE PF AND THE AUTOPLT/FLT DIRECTOR WAS IN USE IN HDG AND ALT MODES. OUR INITIAL HDG FOR THE APCH TO RWY 10L WAS 230 DEGS WHICH WOULD TAKE US TO THE NW OF GRENS NDB. WE HAD DSNDED TO 4000 FT AND ASSIGNED A HDG OF 270 DEGS. DURING THE INITIAL RADAR VECTORS; THE TCASII WAS OPERATING ON THE 12 MI SCALE. THERE WERE APPROX 3 ACFT DISPLAYED ON THE TCASII DISPLAY. I WOULD DESCRIBE THE CTLR'S WORKLOAD AS MODERATE. AT ABOUT 13 DME ICBP W-NW; WE WERE ASSIGNED A HDG OF 180 DEGS AGAIN AT 4000 FT. THIS PLACED AN ACFT AT APPROX OUR 1:30 O'CLOCK POS FOR 3 MI AND 4000 FT. AS THE INITIAL CONFLICT DEVELOPED; I THOUGHT THAT THIS ACFT MAY ALREADY BE ON THE RWY 10L LOC AND HE WOULD PASS IN FRONT OF US. WE THEN RECEIVED A TA FOR THAT TFC. ATC THEN ISSUED A R TURN TO 300 DEGS. AS WE STARTED OUR TURN WE RECEIVED A PREVENTIVE RA; 'MONITOR VERT SPD;' WITH THE SCALE ON THE VSI SHOWING RED BELOW ZERO. THE AUTOPLT WAS DISCONNECTED AND WE STARTED A GENTLE CLB TO 4200 FT AS A LIGHT TWIN PASSED JUST BELOW THE FO'S SIDE WINDOW. AS WE PASSED THROUGH HDG 210 DEGS; THE CTLR ASKED OUR HDG AND GAVE US A L TURN TO 080 DEGS. AS WE STARTED THE TURN BACK; WE RECEIVED A CORRECTIVE RA; 'CLB; CLB' OR 'CLB; CLB NOW.' THE VSI SHOWED RED FROM +2000 FPM AND BELOW. WE COMPLIED WITH THE RA BUT DID NOT ACQUIRE THE SECOND TARGET. THE MAX ALT REACHED DURING RA WAS 4700 FT. THE CTLR REISSUED A TURN TO 080 DEGS HDG AND CLRED US FOR AN ILS TO RWY 10L. WE LANDED WITHOUT INCIDENT. I NOTICED ON THE TCASII DISPLAY THAT THE WHITE 'OWN ACFT' SYMBOL SUPERIMPOSED OVER THE RA TARGET MAKES THE TARGET VERY DIFFICULT TO SEE. THE 'OWN ACFT' SYMBOL AND THE ORIENTATION MARKS ARE DOMINANT VERSUS THE RA TARGET AND ITS DATA TAIL. BOTH THE PROX AND TA TFC SYMBOLS ARE MORE DISCERNIBLE AGAINST THE DISPLAY'S DARK BACKGROUND. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR WAS IN IMC DURING BOTH OF THESE ENCOUNTERS. THESE WERE NOT FALSE ALARMS; HE SAW THE FIRST ACFT ABOUT 200 FT AWAY. THE SECOND ENCOUNTER WAS CAUSED WHEN THE RPTR WAS GIVEN A TURN AND CLBED IN RESPONSE TO THE TA. THERE WAS A LOSS OF SEPARATION; BUT THE RPTR DID NOT SEE THE OTHER ACFT. THE SEPARATION WAS DESCRIBED AS BEING EITHER 0.25 MI OR 2.5 MI; LTSS. THE RPTR CALLED THE TRACON SUPVR IMMEDIATELY WHEN ON THE GND. THE SUPVR ADMITTED THAT THE FIRST INCIDENT WAS 'CTLR ERROR' AND THE SECOND WAS THE RESULT OF THE FIRST INCIDENT. THE RPTR AND HIS FO BOTH 'LOGGED OFF' OF THE TRIP AS SOON AS THEY GOT ON THE GND. THEIR ACR AND PLT'S UNION HAVE BEEN VERY SUPPORTIVE OF THE CREW.