Maybe this trial and error 'tale' will assist others if they try the actions that I FINALLY got to that resolved the issue and then work backwards from there it that doesn't work for them. Just sometimes the simplest possible solutions are in fact the real solutions.
I had pretty much all the above symptoms with my 2007 Equinox (135,000miles on the clock).....Service Stabilitrak/Service Traction Control warnings and check engine light came on one bright sunny morning for no apparent reason. Vehicle drove and handled as per normal. No changes to anything: driving pattern/maintenance/climate etc.. immediately prior to this manifestation.
......searched a hundred plus blogs by means of research (at this point I should point out that I have not been mechanically minded AT ALL for the last 45 years but, as we are stuck in the USVI for a short term with a dearth of even half-decent mechanics or shops that don't ask $50 just to lift the hood!) we had to take matters into our own hands so to speak!
First off, after much reference to internet, I decide to get brave and change the EGR valve. Looked an easy job , even for me. So got one online from Rock Auto........it turned up in good time BUT was (despite website and invoice saying the Dorman product was of 'Origin in USA") made in China and didn't fit properly. Returned it with no problem; good site despite this hiccup. Got a replacement genuine GM part. Problem still existed though.
Then mech hunted down and dragged a 'friendly' mech with a major set of decoder devices to analyse the computer. Got C0561/P1779/P0404. Codes all diagnosed as results above. Odd given EGR replacement, but hey what do I know.
My 'friendly' mech then suggested that a fault in the main 80 amp fuse could produce these results; looked on web saw these going for $23 upwards, hunted round locally and (still my beating heart!) without a great deal of optimism after trying 4 other local autopart outlets decided to drop by the local GM dealer just for a laugh. Expected to be royally stiffed BUT got the last one (yep the last one until the next container ship of parts turns up in 2 months!) for just $13!!! Raced home, well sort of given the roads here, to fit the fuse..........fitted.......no change in lights/code.
Ditched the 'friendly mech' and read chevy blogs online some more, well for almost 24 hours.......... Boy are there a ton, hundreds/thousands of owners suffering from similar problems and getting massively stiffed by Chevy dealers who deny there is a recognised issue!!!
The most sensible course of action (and coincidentally the cheapest!) as recommended on here was to buy some Chevron Techtron Fuel System Concentrate and ALSO (significant!!!) some throttle body cleaner. Given our current location, probable dirty fuel/burn, my gut warmed to this as a solution.
Next day (today, 7th March 2017 in fact) $18 lighter and armed with these 2 cans of 'elixir' I attacked the problem. Obviously the Techtron 'might' take ages to resolve any problems, so I moved on to the TBC.
Heavens decide to open so had to do this in a tropical downpour.........nonetheless it was a very simple and easy job for even a novice like me! My dearly beloved had to interact by depressing the throttle pedal to allow me to clean the gunk off the butterfly valve in the throttle body.......... man there was some real 'crap' in there, looked like dark treacle.........but with the aid of an old toothbrush we got most of it cleaned.
The moment of truth..........turned on the ignition, fired it up....................NO lights!!! Let the idle settle and sort itself out with the onboard computer settings for 5 minutes to............then turned it off. The second moment of truth.......back on no lights................... hallelujah! Still not wanting to believe my layman's luck, I drove off for 20 minutes, parked, stopped, engine off, engine on, no lights!
Repeated process........all still good.......... will only report back if it all goes pear shaped (https://en.wikipedia.org/wiki/Pear-shaped
So.........in summation, check your throttle body out first!!!! Well worth a shot.
With much thanks to all who have contributed either directly or indirectly to me solving this.............thanks guys/gals and shame on GM/Chevy!