How to send HTML emails with images that load from web pages? Ideally with Thunderbird

One way to accomplish this is to turn off "Compose messages in HTML format", which is under your account settings, in "Composition and Addressing". This will also get rid of the HTML editor, which can be useful even for plain-text messages. (e.g., it nicely formats lists)

The other way which preserves the HTML editing features, but auto-converts to plain text, is Preferences -> Composition -> Send Options -> Text Format, select "Convert the message to plain text" instead of "Ask me what to do".

From mozillaZine's Images in messages do not appear :

Ensure that the menu entry View > Message Body As specifies "Original HTML".
If it does so already, switch to "Simple HTML", exit and relaunch Thunderbird.
If the problem is still there, restore to "Original HTML" and relaunch.

If you are still unable to view images :

Messages marked as Junk are normally "sanitized", meaning that they are displayed without any images or other HTML formatting. To change this behavior, go to "Tools -> Junk Mail Controls", click on the "Settings" tab, and uncheck the box for "When displaying HTML messages marked as Junk, sanitize the HTML".

If you are using Thunderbird with a proxy, it is possible that this is the source of the problem. Try adjusting your proxy settings and see if this helps. A few related forum threads are here, here, and here.

Messages composed/sent using a Word/Outlook combination may cause problems. This forum topic suggests that it is caused by Microsoft creating abnormal "content-type" headers for image attachments.

EDIT

The headers in the message you posted are all loused up. Not only is the Content-Type all wrong and appears twice, but the file name has no extension which can be used to control the display.

You should really ask the sender to use a better email client, or maybe him just adding the extension '.png' to the file-name could solve the problem.

Maybe this article would help a bit : How to Edit Received Email Messages in Mozilla Thunderbird. If not, you could try Windows Mail / Outlook which, if it is anything like Internet Explorer, maybe analyzes the attachment by content rather than by MIME type.