How to use auto-updatable templates with Word 2011? I would like to have a template that I can update and be able to auto-update the documents using this templates.

Currently I wasn't able to find a way to convince Word 2011 to update a document based on the changes made to the template.
Just like in the Windows version, this is done via the menu: Tools > Templates and add-ins.
In the dialog box that appears, check "automatically update document styles". And of course set the correct template if necessary.

Each time you open the document, and the template location can be found, the styles will be updated to match those from the template.