Hi Chris,
Gravity forms overwrite email sender/reply-to and its good this way. It works same way how without smtp plugin, you just use SMTP instead your server.
Email out of Gravity forms - forgot password, registration or whatever else exclude Gravity forms will use settings what you have in SMTP plugin.
jodzeee setting Sender as visitor who filled the form its not the best practice regarding ''spam'' these emails can easily finished in spam box.
Good practice is sender as site email - admin whatever what you authorized for that site/smtp and then visitor email (who filled the form) set up as ''reply-to''
About saving entries from submissions, it depend what plugin you use, there are several solutions for that.
