A backup of your customizations is a very good idea. They are not all stored in normal.dot, though! Here is a list for Word 2007 & 2010: https://www.msofficeforums.com/word/...locations.html
For Word 2003 see What Files Do I Need to Backup? (or where does Word store all my customizations?) by Dave Rado, MVP and Brenda Hutton

You can also store your macros and many customizations in a different global template so you don't have to worry about normal.dot having to be reset. This is also a better way to share customizations with others. You would want a backup of that file.

Again, you can't transfer the normal.dot file directly from Word 2003 to a later version. You can use it, you just can't use it to replace normal.dotm.