Windows – Install Windows 7 from external USB hard disk

In Windows Explorer's Folder Options dialog, along with ensuring Show hidden files, folders, and drives is selected, you need to ensure the Hide protected operating system files option is not selected.

This should show you all the Recycle Bin folders/files marked with +H and +S attributes.

You can get rid of the entire $Recycle.Bin folder if you're an admin user or via a Linux LiveCD, but Windows will recreate it once you delete some more files on the same drive.

Rufus developer here.

There's a non publicized cheat mode in Rufus that may allow you to use an external non USB drive like an external USB one, and that's Ctrl-Alt-F. Basically what this does is that it might enable Rufus to list drives that are seen as removable/hot-plug by Windows, regardless of whether they are USB based. Thus, provided that your BIOS/UEFI firmware properly tags them (you may have to fiddle with your BIOS options for that, but be mindful that not all BIOSes allow you to do that), you might be able to use an e-SATA drive.

Now, here comes the BIG DISCLAIMER: The reason why this is a non publicized option is because you will receive absolutely no support regardless of whether the option works or not and also and I make also NO GUARANTEE WHATSOEVER that it'll work for the purpose you want. For instance if Rufus happens to destroy valuable data while using Ctrl-Alt-F, you are 100% on your own. YOU HAVE BEEN WARNED.

I will also point out that this will still result in the whole drive being partitioned and reformatted, so it'll only work if you can dedicate a whole drive. If you want partition preservation then you're on your own.