For anything (except Building Blocks) to store something in a Global Template, you need to open the template for editing. You can find it in your Startup Folder and right-click to choose Open, or you can use File > Open within Word.

When the template is open for editing, you will be given that as a potential location for storage. Generally there is a drop-down for storage locations. This includes QAT modifications.

For AutoText and other Building Blocks, any Global Template that already contains at least one Building Block will be available as a storage location when you create a new Building Block.

• Where can Building Blocks be stored?
• Building Blocks Organizer

As far as moving currently saved customizations...
Moving (Sharing) Customizations in Microsoft Word

Macros you can copy and paste in the Visual Basic Editor or you can use the Organizer. Keyboard shortcuts should be stored in the same file that contains the macro or Building Block. Chris Woodman's Keyboard Shortcut Organizer