C560 FLC HAS ALTDEV AND FMC PROGRAMMING DIFFICULTIES DURING DEP FROM SDL.

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WE DEPARTED SDL RWY 21 USING THE CESSNA PROFILE 'A' DEP PROC FOR NOISE ABATEMENT. AUTOPLT WAS ENGAGED AS THE FMS CYCLED OFF THE DEP END OF THE RWY AND WAS FOLLOWING THE BANYO 4 DEP. UPON CONTACT WITH PHX DEP; WE RECEIVED AN AMENDED CLRNC THAT TOOK US OFF THE SID AND ASSIGNED A HDG TO JOIN A VOR RADIAL. THE PF SWITCHED FROM NAV/FMS TO HDG AND NAV DISPLAY TO VOR #1. VOR DISPLAY INDICATED ACFT R OF COURSE AND ON AN INTERCEPT FOR THE NEWLY ASSIGNED RADIAL. PNF BEGAN UPDATING FMS WITH THE NEW CLRNC. AT APPROX THE SAME TIME; THE AUTOPLT STARTED TO LEVEL THE ACFT AT 3000 FT AND PWR WAS REDUCED TO APPROX CRUISE SETTING. FLT DIRECTOR WAS SWITCHED BACK TO FMS/NAV. THE ACFT STARTED A R TURN TO INTERCEPT THE FMS COURSE. THAT CREATED A DISCREPANCY BTWN WHAT THE VOR HAD BEEN DISPLAYING AND WHAT THE FMS WAS NOW DOING. ATC CLRED US TO 5000 FT AND ALT SELECT WAS SET/CONFIRMED AT 5000 FT. SIMULTANEOUSLY; THE ACFT OVERSPD ALERT CAME ON INDICATING THAT THE ACFT HAD ACCELERATED TO AN ACFT SPECIFIC VNE FOR OPS BELOW 8000 FT. PF SELECTED FLT LEVEL CHANGE ON THE FLT DIRECTOR AND EXPECTED THE ACFT PITCH TO BEGIN INCREASING. THE ACFT PITCH DID NOT RESPOND. PF ATTEMPTED TO INCREASE PITCH ATTITUDE USING AUTOPLT PITCH TRIM WHEEL. ACFT RESPONDED TO NEITHER INPUT. (THESE MODES DID NOT RESPOND WHILE THE ACFT WAS IN AN OVERSPD CONDITION.) AS THE AIRSPD FELL BELOW VNE; THE ACFT PITCH THEN BEGAN TO RESPOND AND THE CLB BEGAN. THIS EVENT ALSO DISTR THE PNF FROM EVALUATING THE FMS NAV INPUT WHILE HE ASSISTED WITH A PWR ADJUSTMENT. AS THE ACFT WAS LEVELING AT 5000 FT; WE RECEIVED ATC CLRNC TO 7000 FT AND ALT SELECT WAS SET/CONFIRMED AT 7000 FT. AFTER ESTABLISHING ACFT IN THE CLB; THE PF WAS HEADS DOWN IN THE COCKPIT EVALUATING/DISCUSSING FMS. FMS PROGRAMMING WAS CONFIRMED AND THE ACFT WAS THEN SWITCHED TO FMS/NAV. THE PF CAME BACK TO THE FLT INSTRUMENTS AND DISCOVERED THE ACFT APCHING 8100 FT MSL. PF DISCONNECTED AUTOPLT; DECREASED PITCH ATTITUDE TO DESCEND AND INITIATED L TURN TO COURSE. AS TURN BEGAN TO THE L; ATC ISSUED A HEADING AND DECENT INSTRUCTION. WE RETURNED TO ASSIGNED COURSE AND ALTITUDE. IN RETROSPECT; THE PRIMARY CAUSE FOR THE DEVIATION WAS THE PF STOPPED BEING THE PLT FLYING! CONTRIBUTING FACTORS WERE: HIGH RATE OF INITIAL CLB FOR NOISE ABATEMENT. THE IMMEDIATE CHANGE OF THE ATC CLRNC UPON DEP WHICH LEAD TO A REPROGRAMMING OF THE PRIMARY NAVIGATION PMS. THIS OCCURRED DURING THE CRITICAL DEP PHASE WHILE STILL CLOSE IN TO THE ARPT. HIGH VOLUME OF VFR TFC IN VICINITY OF DEP ARPT CAUSING DIVISION OF ATTENTION BETWEEN INSIDE AND OUTSIDE THE ACFT. HIGH COCKPIT WORKLOAD; SWITCHING FROM FMS TO VOR BACK FMS; QUICK STEP CLIMB; IN ABILITY TO RESOLVE THE PROB OF WHICH NAV SYSTEM WAS CORRECT; VOR AND FMS. EFB OF PF HAD 'TIMED OUT' AND WAS BLANK. THIS CONTRIBUTED TO THE INABILITY OF THE PF TO VALID DATA WITH THE PNF. ATC WAS VERY BUSY. LITTLE BREAK IN TRANSMISSIONS TO ATTEMPT TO VERIFY CLRNC. EXPECTATIONS THE FMS DATA FOR NAVIGATION WAS JUST A KEY STROKE AWAY AND CONTRIBUTING TO FOCUS ON GETTING THE FMS PROGRAMMING TO NAVIGATE THE NEW CLRNC WHEN VOR DATA WAS READILY AVAILABLE AND ONLY NEEDED TO BE VALIDATE AS CORRECT TO BE USED. AN EXPECTATION AND RELIANCE ON THE AUTOPLT TO CAPTURE THE ALT SELECT. ALMOST CONSTANT ATC COMS AND INTER-COCKPIT COMMUNICATION CONCERNING THE NAVIGATION PROB WAS COMING OVER THE HEADSETS AND PROBABLY COVERED THE ALT ALERT TONE. IT WAS NOT HEARD BY EITHER PLT. UNKNOWN REASON WHY THE AUTOPLT DID NOT CAPTURE THE ALT SELECT. IT HAD CAPTURED THE TWO ALTS PREVIOUSLY ASSIGNED AND CONTINUED TO CAPTURE ALTS AS SELECTED DURING THE REMAINDER OF THE FLT.