Difference between $numpages & $max_page on archive pages

First, let’s go through variables one by one:

1. $numpages is set on each setup_postdata() call. It becomes either 1 or number of pages in multipage post.

2. $max_page doesn’t seem to be global at all. I don’t see it referenced as such in code and from quick test it is not getting set on archive page for me.

3. $multipage indicates if current post has multiple pages (in other words if $numpages is larger than 1).

Where do they come from?

Mostly setup_postdata() as you have discovered.

$multipage get’s set to 0 if the $post->post_content is already an array

It does not. It gets set to 0 if $post->post_content does not contain any <!--nextpage-->.

Why do I have $numpages on archive templates/pages as it is only meant to be set for paged content types?

Because any loop sets it (in setup_postdata() call) and it remains set. It’s like calling something after the loop that was not reset – globals still hold whatever post that was looped through last.