for the image to display in the email, it will need to use a full url, you will need to edit the image tag added by HTML editor after the image is added.
click the HTML editor source button, and change the image src attribute from a server relative path:
</img src="/path/to/images/image.jpg"/ >
to the full http address to the image:
</img src="http://www.mydomain.com/path/to/images/image.jpg"/ >
for the quotes problems, there is probably formatting applied to the initial value of the html editor instance.
Edit the HTML editor instance on your page, click the lightning bolt next to initial value, and reselect the corresponding recordset column.