A Case of a Lost File. PLEASE HELP!!!

The "New Folder" on the sidebar is irrelevant as the sidebar is effectively just a bunch of aliases. You made a "New Folder" on your desktop. That's the one that matters because that's the only "New Folder" that really exists. If you deleted that one, then the files you copied into it would also be gone.

Additionally, no, dragging a file isn't a "cut and paste" operation. It's a really bad analogy because it doesn't always apply. If you drag from one drive to another, files are copied. If you drag within a single volume, files are moved. Therefore, if you were copying files from your external drive to your internal, they would still be on the external unless you did something special to remove them.

 

Plus unlike Windows folders REPLACE not MERGE.

 

Where did you create the "New Folder"?

My guess is that it was within the external hard drive's window, so it exists ONLY on that external and would indeed disappear when you ejected it. I can almost guarantee that it you plug that external back in, the 'New Folder' will show up once again.

Make a new folder in a brand new Finder window or on the Desktop and then use that folder...i.e. drag that one to the sidebar and use it for storage/transfer of these files.

EDIT: I am more convinced this is what happened to you after re-reading because simply dragging files from one drive to an other makes a copy on the destination and keeps the originals in place, but when dragging files from one folder to another on the same drive, it removes them from the original location and they end up in the new spot. So, if you truly made a 'new folder' on the main drive (on the actual desktop as you say), dragging files to it would not have deleted the originals without holding down an extra key.