In regard to the save and continue funtion, is there a way to send an automated series of mails to encourage the user to finish a form? Can this be done with gravity or mailchimp?
If you add them to your Mailchimp list, Mailchimp can send a series of automated messages via email, with whatever content you want. Gravity Forms itself won’t send a series of emails on any schedule - by default, there is only one email sent after the progress is saved with the save and continue functionality.
See this filter for an example of how to trigger a Mailchimp feed when a partial entry is saved: