Can I assign steps and send notifications to the form submitter?

Yes. The form submitter does not need a WordPress user account. 

If the submitter will have a WordPress user account then you can assign the step to the User (Created By) field. If you don't see the 'User (Created by)' field in the 'Assign to' setting, go to form settings and activate the 'Require user to be logged in' setting in the 'Restrictions' section of the form settings.

If the form submitter will not have a WordPress account you can assign the step to an email field.