How can I send an email from the D7 UI to specified email addresses?
I want to type in some text, type in some recipient addresses, and click send to send it from the site's address.
An easy way could be using Rules and a custom content type.
The content type should have a title which can be used as the email title, a body for email body, and a field to hold email address(es) (or perhaps a reference field to site users or roles).
Then configure a new rule. Select new content event, add a filter to restrict to defined content type, then as an action select send email. Map the proper inputs and you are done.
There are innumerable ways to accomplish this. If you don't need to track the outgoing mail (keeping a copy on the server), I would do it this way:
in a custom module, create a custom form containing the email elements (to, body, etc) inside a custom page
use a module such as Simple Mail to create the actual mail
A module to simplify sending emails with Drupal.
There are many great modules for complex email handling and sending scenarios, or email templating, and Drupal core handles emails pretty well by itself. However, for many sites, a radically simplified email sending system is helpful.
This is probably a more advanced method fo accomplishing this, but if you haven't yet, and want to get into custom module creation, this is farely simple and would prove a good starter project. This has an advantage of being small and lightweight
Drupal isn't exactly meant as an email client, instead try doing it in a Drupal way.
For example: