AN LR25 PIC ENCOUNTERS MANY DIFFICULTIES WITH ACFT CTL DURING A 3 LEG TRIP TO OMA; NE.

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I HAD A BAD NIGHT. I WAS TIRED. I MADE NUMEROUS ERRORS THAT WERE OBSERVED AND RPTED BY 2 INSTRUCTOR PLT/CHK AIRMAN SITTING ON THE JUMP SEATS. MY JUDGEMENT AND THOUGHT PROCESS WAS IMPAIRED AND I DID NOT REALIZE IT AT THE TIME. AT THE SAME TIME THOUGH; THEY DID NOTHING OVER THE 3 LEGS TO STOP ME. THE ACFT WAS NOT DAMAGED; BUT I WAS CALLED UP IN FRONT OF THE DIRECTOR OF OPS AND RELIEVED OF DUTY FOR 7 WORKING DAYS. IN OUR COMPANY WE HAVE A CORE VALUE 'OPEN AND FREE COM' THAT OBVIOUSLY BROKE DOWN HERE. I ALWAYS THOUGHT I WOULD REALIZE I WAS TOO TIRED/STRESSED TO FLY BUT I DIDN'T. I HAVE FLOWN NIGHTS FOR OVER 3 YRS AND HAVE ALWAYS FELT TIRED; AND APPARENTLY I HAVE TO READJUST MY GAUGE TO FIGURE OUT WHEN I AM TIRED. I KNOW I AM NOT ALONE. WHILE APCHING CPS WITH THE PIC FLYING; ACFT WAS BENEATH THE LATERAL LIMITS OF CLASS B AIRSPACE THE AIRSPD WAS ALLOWED TO BE 250 KIAS. WHILE CIRCLING AT CPS; THE ACFT WAS ALLOWED TO CLB 200 FT HIGH REPEATEDLY PUTTING THE ACFT IN THE CLOUDS ELIMINATING VISUAL REF TO THE RWY FOR EXTENDED PERIODS. THE SIC ADVISED THE PIC TO GO AROUND ON 2 OCCASIONS THEN THE PIC RESPONDED IN A FORCEFUL MANNER 'I KNOW WHERE I AM.' BEFORE DEP FROM CPS; OTHER QUALIFIED CAPT OFFERED TO FLY THE OUTBOUND LEG BUT THE PIC REFUSED THE OFFER. WHILE APCHING MKC; WITH THE PIC FLYING; AT LEAST A 360 DEG TURN WAS MADE EITHER FOR SPACING OR TO LOSE ALT WITH SPOILERS. INITIAL ALT WAS 2600 FT MSL BUT THE PIC DSNDED TO 2400 FT MSL; THE SIC ADVISED TO CLB. UPON LNDG AT MKC; HVY BRAKING WAS USED CAUSING THE ACFT TO SLIDE TOWARD THE L SIDE OF THE RWY. IT APPEARED AS IF A HIGH SPD TURN OFF WAS BEING ATTEMPTED. HOWEVER; NONE WAS AVAILABLE. THE ACFT WAS SIDEWAYS ENOUGH THAT WHEN THE PIC RELEASED SOME BRAKE PRESSURE; THE ACFT RETURNED TO THE CTRLINE. RWY WAS WET AND 7001 FT LONG; REVERSE WAS AT IDLE DEPLOY. WHILE APCHING TO LAND AT OMA; WITH THE PIC FLYING; THE ACFT WAS TOO HIGH AND TOO CLOSE TO ARRIVE AT THE INITIAL ALT AT THE APPROPRIATE POS. ATC QUERIED ABOUT BEING ABLE TO GET DOWN IN TIME; RESPONSE WAS TO THE AFFIRMATIVE. ATC WAS ALSO REQUESTING THE FLT TO SLOW FOR SPACING. PIC FINALLY WAS USING 6000 FPM AND 280 KIAS FAF INBOUND WITH FULL SCALE GS DEFLECTION (ACFT HIGH). SIC ADVISED THE PIC TO GO AROUND AND FINALLY THE PIC AGREED. ATC ADVISED TO CLB AND MAINTAIN 3000 FT MSL. HOWEVER; THE PIC CLBED TO 3400 FT MSL AND REACHED OVER TO TURN OFF THE MODE C. UPON LNDG AT OMA; HVY BRAKING WAS USED. THE PIC ALLOWED THE ACFT TO SLIDE SIDEWAYS TO THE L. THE FLT WAS GIVEN DISCRETION FOR THE INITIAL DSCNT DESCRIBED ABOVE. RWY WAS WET AND 9500 FT LONG; REVERSE AT IDLE DEPLOY. IN ALL SITS LISTED ABOVE; THE WX WAS IMC.