1. The answer to your question is "use Windows Explorer or My Computer". It's cut/paste or copy/paste or drag/drop or drag/drop+shift or using the copy or move icon in the toolbar (if you set the program to show those). Delete separately if the method you choose doesn't do it.
Moving file around like this is VERY basic use of Windows.

2. Portable drives are rather error-prone. If you delete the original, don't burn it to CD or DVD and have your only copy on the portable drive, chances are that you are going to lose them all in a few years. That might be something you don't want. So take care!

Kees