A PLT ON DEP EXPERIENCES A TCAS RA AND A DISCREPANCY IN THE FMS.

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I FLEW IN AND OUT OF LAS VEGAS TWICE IN 1 DAY. OUT OF 4 LEGS; I HAD PROBS WITH MY FMS. COMING FROM THE E I HAD NO PROBS; BUT FLYING THE IDALE 2 DEP I HAD MANY PROBS. ON DEP I HAD 2 RA'S AND I WAS FLYING WITH MY MAP DOWN 2.5 MI. I DID NOT TELL CONTROLLERS I WAS LOOKING FOR TFC FOLLOWING RA COMMAND AND RADIO WAS VERY BUSY. IN THE MEANTIME CTLR TOLD US TO GO DIRECT IDALE; WE PUSHED BUTTONS ON FMS TO GO DIRECT TO IDALE. I DID NOT CONFIRM ON THE MAP FOR SOME REASON; THE INFO WAS NOT RIGHT IN THE FMS BOX. AT THE SAME TIME WE WENT UP TO 7300 FT BECAUSE OF RA'S. WE WERE TO GO UP TO 7000 FT. I DO NOT KNOW WHAT HAPPENED TO THE FMS AND IT WAS A VERY BUSY TIME ON DEP. COMING BACK TO LAS VEGAS AFTER FUZZY INTXN ON THE ARR THAT STARTS WITH A 'T;' THE MAP JUMPED FMS SAID CHK POS. THE CTLR ASKED WHY I TURNED. I TOLD HIM I HAD FMS TROUBLES AND TOLD THEM I HAD VISUAL WITH ARPT SO THAT I DID NOT TRUST FMS. ON LEAVING LAS VEGAS ON THE IDEAL 2 I WAS VERY NERVOUS AS TO WHAT WOULD HAPPEN. THIS TIME ON DEP A HAWKER WAS HAVING TROUBLES ON THE DEP. THIS TIME WHEN THE FMS WAS ACTING UP I PUSHED HEADING SO THAT WE WOULD NOT GO OFF COURSE. THEN I STARTED TO TROUBLESHOOT AT WHAT WAS GOING ON. I HAD ONLY 1 VOR (BLD) AND NOTHING ELSE; NO DME; NO OTHER VOR. I WENT TO SATELLITE PAGE AND I SAW 5 AND THE NUMBER WAS GOING UP AND I WAS WONDERING IF I HAD LOST ALL THE SATELLITES. LAS VEGAS IS SO CLOSE TO A LOT OF MIL AIRSPACE. WERE THEY DOING SOMETHING? I FLY ALL OVER THE USA AND I HAVE NOT HAD ANY PROBS WITH THE FMS.