Do you save and archive all of my sent emails?

Yes, any email sent to your contacts will be organized by name and date sent. By going to the Communicate menu > Emails, you'll find the list with all of your draft emails, scheduled emails and sent emails.

Also, you can find your sent emails archived by client if you go to the Contacts menu > Contact name > section 'Other Communications' > link 'View All'  and apply the 'Emails' and 'Direct emails' filters.