It sounds as though you may be confusing cPanel with your FTP program.
cPanel has a file manager and a legacy file manager. In the file manager you just select a file and click on the download icon or link in the icon ribbon.
It won't let you download folders. For that you would compress them and download the zipped or tarred archive. Sounds like you had some problems with your backup, which you'd need to sort out your end. But this is the normal way of moving sites around so well worth cracking the problem. And you'll find lots of threads from people who've gotten themselves into trouble and regret not having a valid backup.
In a typical FTP program you'd have your local file system in one window and the remote one in the other and just drag files between them.
And just to underline DrByte's advice, don't every edit PHP files with a word processor - they insert extra information and structure into the files that can corrupt your site when loaded back to it.
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