You CANNOT save a document or another template as the Normal Template and have a fully-functional normal template. I think you have discovered that.

See if you can recover your old normal template. There may be a "Backup of Normal.wbk" file. If you can't chances are good that your keyboard shortcuts and macros are gone. (They were likely in the Normal.dot file that you deleted.) If you find that file, with Word closed, rename your current Normal.dotm file to something else and remember the name. (It has your styles, I believe.) Then rename the backup file to Normal.dotm. Restart Word. Are your macros now available?

By default, recorded macros are stored in the Normal template. That is not necessarily the best place for them but it is the easiest. You can, and IMO should, store your production macros in a separate Global Template (or multiple such templates). Any keyboard shortcuts to those macros should be stored in the same template as the macro. Keyboard shortcut, too, are stored in the Normal template by default.


See also: Moving (Sharing) Customizations in Microsoft Word

For styles, many should likely be stored in document templates. You can have multiple organizations of your [Quick] Styles Gallery using [Quick] Style Sets. They make it easy to update documents and other templates.