Hi,
Out of the box Gravity Forms doesn't save partially filled forms. You might try Gravity Forms Data Persistence (http://wordpress.org/plugins/gravity-forms-data-persistence-add-on/) and see if that suits your needs.
As far as the PDF portion of your project goes, yes. Our plugin can do what you need. Please see our documentation on installation and configuration - http://gravityformspdfextended.com/documentation/.