Use Amazon SES to send emails with embedded images and arbitrary headers.
As long as the 'override wp_mail' option is checked, everything should 'just work'.
You can, but it won't work everywhere. For delivery to many clients, including Android GMail and iPhone Mail, you need to attach a copy of the image to the email.
There's some details on how it works here at StackOverflow. This plugin basically handles all that header creation palaver for you.