Question: Should an HTML email message begin like any valid HTML-document and should it even have a DOCTYPE declaration?

Answer: 
HTML emails should include a doctype, html and body declaration if you intend to do anything fancy at all.

There are a multitude of guides on this subject which can help you learn how to properly code HTML Email, but most of them disregard the specifics of a doctype, which is how I stumbled on your question.

I suggest you read the following 2 posts which are from reputable teams familiar with the various problems:

[campaign monitor's take](http://www.campaignmonitor.com/blog/post/3317/correct-doctype-to-use-in-html-email/)

[email on acid's take](http://www.emailonacid.com/blog/details/C13/doctype_-_the_black_sheep_of_html_email_design)
No, since most email clients strip out the `<html>` and `<body>` tags and replace them with their own (see hotmail).

As for the doctype, see: <http://www.campaignmonitor.com/blog/post/3317/correct-doctype-to-use-in-html-email/>

Assuming you're using a table for your layout (you should be) you'd have one all encompassing table that effectively acts as your `<body>` element, and then nested within you'd have the rest of your content positioned within other tables.