Windows XP
 

All night the Defragment program was stopped:

[c:] Paused for Volume Shadow Copy

I restarted the program and the same thing popped-up.
Never saw this before. What is it?

I can't say that I've seen that message before. You could stop the Volume Shadow Copy service while it's running and that ought to take care of it. However, I recommend using Defraggler instead of the built-in defragmenter.
https://www.piriform.com/defraggler
It's small, fast, effective, and robust.

Before the Defrag, I ran CCleaner and deleted;

Internet Explorer:
temporary internet files
cookies
history
recently typed URL's
Index.dat files
last download location

Windows Explorer:
recent documents
search autocomplete
other explorer MRU's

System:
empty recycle bin
temporary files
clipboard
memory dumps
Chkdsk file fragments
window log files

So, the question is, if some of the above was a no-no?

The error you got was not related to anything you did with CCleaner.

Volume Shadow Copy is a background filesystem subsystem that helps Windows do backups of files that are in use and allows Windows Vista and later to keep backups of files when you change them.

If they are necessary, how do I get it back?

You mean if you need to retrieve an older version of a file that you changed? In XP, there's nothing you can do. XP doesn't keep backup versions. It only uses the volume shadow copy service if you're using a backup program.

In Vista, you can use this:
https://www.shadowexplorer.com

I could go back a week on Carbonite.

Turn off the restore points in your system properties then restart, that should take care of it.