Based on the Account settings of the individual sending the envelope, this determines whether or not a Recipient has to create or has to have a pre-existing DocuSign Account to sign a document. The setting is under the Account "Security" and is under the header "Login Requirements". Set to "Not required to login" allows any Recipient to sign without having a DocuSign Account.
Recipients (if they have a DocuSign Account) have the ability to disable Notifications. As a Sender you cannot disable the Notifications that go to a Recipient.
At an Account level you can disable the final attachment that goes out to Sender and Recipients after the envelope completes but this is an Account setting so it affects all envelopes sent from the Account.