Drupal Gardens: is it possible to install a new theme?
Drupal Gardens is really limited and you cannot install a theme from drupal.org but what you can do is to customize the possible "layouts" that Gardens give to you.

If you click on the layout button on the panel you will see different layouts (columns and sidebars) and from this basic structure you can start applying custom CSS. Check more here http://www.drupalgardens.com/documentation/themebuilder/layout-tab and http://www.drupalgardens.com/documentation/themebuilder/advanced-tab