I have a downloaded copy of P.T. on my PS4 and want to save just P.T. onto a USB drive. Is there a way I can just back-up P.T. without having to uninstall every other game on my PS4's harddrive?
According to this post, unfortunately, it looks like you cannot only backup a single game. You can backup saves, though.
In theory, you can use an External Hard Drive to do a complete system backup. This complete backup will actually back up games themselves, as well as updates, downloads, game saves, system settings, etc. However, the only utility of this is to restore the backup.
You can't use this to extract a single game off and install it another PS4. Also, whenever you do a restore, it will completely wipe what is on the PS4 at the time. So this should ONLY be used for the sole purpose of backing up your entire PS4 in case of system failure, getting a new PS4, or before you send it off to get repaired.
It seems like this is to prevent copies of downloaded games from being distributed illegally.
Note that there's an option called Extended Storage available for some time now. While not technically being a backup, you can move apps between disks, freeing up space from the main drive. Only PlayStation systems will be able to read those files, which means you can't share storage between PC and your PlayStation system. Other PS4 systems will work just fine, but only if the app is was purchased for the logged-in account.