Moving and/or backing up "Previously Relocated Items"

Where should I relocate this folder, if need be

Store you documents in your Home folder. There are already subfolders for groups like Documents, Pictures, Movies, etc.

You can create your own folders inside your home, too.

. I need to add a new external hard drive for Time Machine as the current one is full and needs replacing.

If your backup drive is full, and you are replacing it with a new one, then it should ask you if you want to use it with Time Machine the first time you connect it to your Mac.

You can also open Time Machine preferences and click Select Disk to add the new drive to your list of destinations.

While in there, you can remove the old drive.

In both cases, it will warn you that it will format the drive, erasing everything on it. That should not be an issue with a new, empty drive.

I don't know whether it must. It may be a permission issue where it must make a copy to give you ownership of the files, but I'm not sure.

You can hold down the command key when you drop the folder which should toggle copy/move behavior (green + badge should disappear). If it allows you to move, it may not fix the ownership, but we should be able to fix that after the move.