> If that's the case, should <h> be required to be the first child of 
> <section>?  If it's not the first child, is it still the heading for any 

I presume that has been done as a concession to semi-presentational
use, such as putting navigation menus before the heading.

> 
> <section>
>    <h id="logo" src="...">The World Wide Web Consortium (W3C)</h>
>    <h id="slogan">Leading the Web to Its Full Potential...</h>

If you did this as Hn, it would be interpreted by user agents that
attempt to model the heading structure as an empty section, followed
by a section entitled "Leading...".  Sub-headings have always been
something of a problem, and are one of the cases where <br> has
traditionally been used.

> <section>
>    <h1 id="logo" src="...">The World Wide Web Consortium (W3C)</h1>
>    <h2 id="slogan">Leading the Web to Its Full Potential...</h2>

No.  That has traditionally, from before HTML, been treated as 
a subsection.

>    <h id="logo" src="...">The World Wide Web Consortium (W3C)</h>
>    <p id="slogan">Leading the Web to Its Full Potential...</p>

The sub-heading isn't body text.