Notification upon email change
Not out of the box, no.  As far as a feature request - I think that this would be a good extension, but might not make sense in core CiviCRM - most CiviCRM installations don't even have uses where their contacts log in, let alone change their e-mail addresses.

To implement as an extension, a developer should use the hook_civicrm_pre hook on the Email entity - it's important to use "pre" and not "post" because otherwise the old e-mail address is already overwritten!  Confirm that the change is driven by that person, not a back-end staff person (my comparing the logged-in user ID to the contact ID that owns the email), and if so, send a custom message to both addresses.  I have an extension somewhere that lets you specify a CiviCRM template to send - the advantage being that a staff person can change the e-mail.  Let me know if you need that posted on Github and I'll track it down.