How to send an eMail notification when a specific field of a node or user has been changed?
You can use the Rules module for this. Here are some details about how to do so:


Rules Event: Before saving content.
Rules Condition: Compare the value of the specific field, for both the original value (before editing the field) and the (new) updated value, to verify if they are different.
Rules Condition: Send an eMail (which is typically implemented as a separate "Rules Component" (that is invoked as the Rules Action), whereas you pass the values like node id, current user, maybe author, etc. Within the Rules Component, you then compose the actual eMail (template) that you want to be eMailed. For an example of such a Rules component, have a look at my answer to "How can I set a reminder for a specific user to be triggered on a specific date?" (which includes such component in Rules export format also).


Should be straight forward to "develop" such rule, no (PHP) coding at all involved (only site building using admin UI).