For the Drupal Garden's style setup, you should definitely look at Aegir. It requires a bit of setting up, but there are loads of tutorials and screncasts - there are a couple of good ones here and here.
With regards to your menu question, that seems like a simple permissions question. When you deploy your new sites, you'll obviously have to set up a user for the owner of said site. If you ensure that user has a particular user role, you can set permissions at "/admin/people/permissions" for the core menu module. Look under Menu around halfway down the page and check the box for
Administer menus and menu items for your site owner's user role.