Menu question

I don't know much about Taxonomy Menu Block, but you can make blocks appear wherever you want by selecting the region on admin/blocks.

Without mentioning Taxonomy it is possible to do what you want just using the Primary and Secondary Links Menus. In admin/menu you would populate the Primary Links Menu with your topics and subtopics (nested appropriately). Then you need to make sure that your Secondary Links are drawn from your Primary Links by going to admin/settings/menu (both of the drop downs should say Primary Links).

Now when you select something from your primary links the appropriate subtopics will appear in the secondary links. You can modify your theme to make the menus appear where you want, or even create a block with some custom code like this, to increase flexibility:

<ul id="secondary">
<?php
  $secondary_links = menu_secondary_links();
  foreach ($secondary_links as $link){
    print '<li>'.$link.'</li>';
  }
?>
</ul>

Hope that goes some way to give you an insight into what you want to do.