How can I get the parent author from sprout forms to send to sprout mail?
This can be done using an Invisible Field and the addFieldVariables tag.  Define the value you want as your email in your template:

{% do craft.sproutForms.addFieldVariables({
    'secretEmailAddress': entry.author.email
}) %}


Set the Invisible Field to target that value:

{secretEmailAddress}


And then customize the Notification Email Recipients field to target the handle of the Invisible Field:

{invisibleFieldHandle}


Another example of doing this dynamically from an Entry with a Form Relations field has been posted in response to another question here: https://craftcms.stackexchange.com/a/29553/115