Time Machine Backups
Thanks for the help. The problem turned out to be both more complicated and simpler than I originally thought.

I had installed a Tar Disk in 2015 and more research showed that quite a few users were having the same problems and error messages as I was.

I followed the instructions here - https://www.tardisk.com/pages/uninstall-sierra - to uninstall the Tar Disk - NOT removing it because I was coming from High Sierra, as the instructions said. It DID NOT solve the problem.

I then went through the whole rigamarole again; shut down my MacBook and physically removed the Tar Disk. I then reopened the Disk Utility and reformatted the internal Mac SSD - installed Mojave from a USB and it seems to have worked.

To answer my PRECISE question - now that Mojave is installed - Time Machine has been able to recover/reinstall all of my files and programs

Thanks again to those of you who responded