When DQX Adminmenu enabled, the Region list of the block page become "static" (same for each enbled theme)

Thanks for reporting.
I do have some idea why this happens.

There is some stuff I need to get out of hook_init(). That's not so easy, but I will try.
One solution I would like would require a new module dependency.. bad.

Ok, my guess was right.
Removing the "drupal_get_form()" from hook_init() does solve the problem (and might also solve other problems, yet unknown to us).
This drupal_get_form() is part of the mechanic that prevents csrf attackers from doing a "flush cache", or "toggle developer modules".

Solution:
I would like to avoid introducing a new module dependency, but this is really the cleanest solution.
The new module is "pageapi", which is yet to be uploaded on drupal.org.

I might do this tonight, or next week, or..

A solution is on git, will be in the next -dev release.
This will have pageapi as a requirement.
Please help testing this, before I make it an official release.

Are you sure? That's impossible.
w/o pageapi there should not be any admin menu showing up.

Duh.
The 6.x-3.x branch was not even pushed online. So you were sitting on the 6.x-2.x...
The 6.x-2.x does not have this problem, but it also does not have the CSRF protection for things like "flush cache" or "toggle developer modules".

A snapshot for 6.x-3.x will be available soon.

This should be fixed since a long while in the 6.x-3.x branch.