Time Machine Backing up Externals

Try the following:

Disconnect drive C from your Mac to simulate a situation where the drive is not available or has failed

Open Time Machine and go back a few days to a point where the drive was connected

On the main Finder window, look for the name of your Mac under the Locations heading on the left panel.

Click on the name of the Mac and another window will open on the right to display Macintosh HD and the name of the external drive

Right-Click on the name of the external drive and you will see an option to "restore to" the hard drive to another destination that you choose

Select the destination......another drive or the Mac's desktop, etc...... and then click Restore

If you don't want to Restore the entire drive, you can open the drive and then select the files that you want to Restore by right-clicking on them.

You're safe. If your drive is not connected when you enter time machine, it won't display the information as there wouldn't be anyplace to which it would restore. You can "see" the complete backup by drilling into your Time Machine disk and folders.

Now, another issue is that a few months ago my desktop and documents (I think those were the two) started syncing with iCloud (I think--I know I should know, but I hit the wrong button at work (elementary school) and it started firing files over the network lol. I've noticed that those options are grey in time machine, too. Probably same deal, right?

Sorry, not sure what you are asking. Time Machine has nothing to do with iCloud and vice versa.

Please read my reply above......which assumes that you do not have the hard drive at the time, or the hard drive has suddenly failed.