Just finished another 2 hour session on phone with Support and they finally found the issue :-)
For some reason there was a time mismatch in log files (~/Library/Logs/amt3log) when opened in Console and the current OS time/clock set automatically by my timezone.
Somehow the supporter managed to align the time so it was right in both the OS and logs (not sure how but running some terminal commands etc.)
So everything seems to work now and I am a happy Adobe user again :-)
I just managed to get the apps running again. After two days, about 10 hours of flailing around with Forum questions and Google queries, I finally gave up and did "Chat"twice, for two slightly different issues. It was the only solution that actually worked. I had gone through the Trash this, Trash that, Go to the library (which one?) and change permissions on this or that file. All BS. None of it worked.
Specifically, the first problem was: As usual, I opened CC on my desktop and downloaded the 3 apps I needed, PS, AI, and ID, (note that I forgot about Acrobat Pro.) but when they installed it was as Trial versions. At Chat, it took the tech about 10-15 minutes of taking over my computer and trashing a whole lot of files and folders to fix it. He or she worked fast, too. He or she had obviously had plenty practice. That fixed the basic download and install problem, then I found that I had a similar problem with Acrobat. Back to the chat page. To heck with hours of scouring the web for answers. The Acrobat problem was: install stopped dead at about 42% and gave up, citing errors DW003 and DW006. I suggest that the chat or phone system is the only way to fix this screwup. Maybe overburdening Adobe's techies will send a message.