Thank you all for your kind responses.
Right after posting my last above post, closing my browser, and waiting a few seconds for the sandbox to empty, I rebooted. And the "Failure to configure Windows updates" loop began again! How did Windows updates start again after I had disabled it?
After tweaking everything I let HP run its "Tune-up" option to round things off. Little did I know that that enabled the Windows Updates automatic download and install function...
I tried to use my System Image Backup saved on my external hard drive, but no dice again. Refresh no dice either, nor System Restore. It might have been those already downloaded but waiting in line to be configured updates that interfered.
So I had to reformat AGAIN! Forth time in a few days. I can't believe it. Getting to D: I couldn't, but luckily my flash drive with the factory image worked.
I found out that in Windows 8 you have to do a series of things to make and use System Backups that are not needed in Windows 7.
This is for Windows 8.1 but similar to 8, and after doing this you must change the boot sequence and use a recovery disk (or flash drive I suppose):
"Create System Image Backup of Windows 8.1 and Restore from it"
I'll stick to making System Restore points. And in an emergency use Refresh. It will work as long as I have updates disabled. And I'll make sure of that. No more HP "Tune-ups."
As for bringing my notebook back to the store, I would rather not have to go through hours of getting my machine in the all tweaked state it is again in now. I like my current Windows 7 look and feel even though it runs on Windows 8. Besides that my Compaq CQ58 was only €329. Can't find a lower price for a 15.6" notebook that works fine (except for needless Windows updates in my case.)
Again, those security updates are not needed as I've never gotten any malware on my notebook by always surfing and opening my mail sandboxed by default. There are Sandboxie users who for years have not had any AV on their systems without ever getting malware. Although the developer of Sandboxie -Tzuk- strongly recommends to use AV for just in case. He told me once during an email exchange that it only happened a few times a year that someone had found a way to penetrate the sandbox wall. And that he always quickly had found a way to close it. So the chances of getting infected are very slim, almost nihil. Even more so with the excellent AV I have.
But thank you for your kind concern.
I still have not gotten a reply to my last question to Artyom Zorin:
"So do I understand it well that you mean not to touch the UEFI? To use the default option with Secure Boot enabled? (Only disabling that latter one when installing Zorin, but after that enabling it again.)"
To me that is an omen not to continue with the Zorin experiment. At least not for now. I'm glad things work and look fine again on my laptop.