Your site will look like the following in a mobile device. The logo will be featured at the top. You can create Dropdown Menus from WP-Admin > Appearance > Menus but that will be applicable for all devices. If you want any jQuery Menu or something else those will be required JavaScripts, CSS3 etc which is complex to implement. The Theme has no option at this moment to implement those easily.
The Theme was updated today. You should Update the Theme. Updating will not delete your posts, pages, news, menus, widgets, settings etc.