How do I remove a folder and keep the stuff inside it?

You can drag the entire folder to the Desktop, then open a window where you wish to move them and drag the folder from the Desktop into that window. If you don't want the files in a folder, then open the folder and drag the files into the window of the new location.

Are you saying that the folder is on a different drive than where the Desktop is? If that's the case then you can open a new Finder window for the same location by pressing the COMMAND key then double-clicking on the folder. You can then "move" the files to the higher level. A copy on the same drive is actually a "move" not a "copy." A true copy occurs when you do the drag and drop from one drive to another. To "move" files from one drive to another hold the OPTION key down when you drag to the destination.

A "move" is the equivalent of first copying the files to the destination then erasing them from the source.