Menu permission/visibility control I am in involved in developing a site builder using Drupal 7.  Since it is a site builder, I need a user to be able to create menu items based on their needs, and then edit those menu items - but not any other users.

Also, is it possible to create a sub-domain during sign-up (along the lines of Drupal Gardens)?
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.