how to move things off the desktop without deleting them

Finder can show you more than one Window at the same time, and you can drag and drop between windows.

Open a finder Window. navigate tot your folder named desktop

Choose New Folder off the Finder's File menu. If you hold Command when you click on the window TITLE, it will let you navigate UP the directory tree to your YourUserName folder. Park that folder on the other side of the display.

Drag (for example) the g4 folder -- likely from your old G4 computer -- to the YourUserName folder. It instantly moves off the Desktop and into the top-level of YourUserName folder. A great place to park it.

Yes, you can move those files around elsewhere:

a) drag and drop them into a folder ON the desktop (i.e., a new folder created inside the Desktop folder in Finder)

b) drag and drop them into a folder anywhere else you have access to, such as your Documents folder or your Public folder.

c) drag and drop them into a folder in the Userid named "Shared", created by default.

You do NOT have access to top-level on the Boot drive, and control is even tighter in later versions of MacOS. The System owns that, and does allow Users to park things there.

You say there are things on your desktop you can't remove? What items are you referring to that can't be removed? Are they files, app, or disk icons?

Files can be put on the desktop indefinitely. You can adjust the Finder settings to hide the Macintosh HD icon if that's your preference. If you have external drives connected, you can right click on the desktop icon and eject them... Just kinda curious about exactly what's on your desktop you're concerned about?