Can "Demonstrate block regions" use a specific template?
In order for a region to show up on the demonstration block, you need to define it in your theme's .info file and print the region in page.tpl.php (or the overrided version). The following could be the issue 


Cache is not cleared (i.e. drush cc theme-registry if you are using drush) 
Theme's .info file has not listed the new region 
Page template is not overrided properly 
The region is not printed properly in .tpl.php file 


I would say, have a look into guide on how to override a template file prpperly here https://www.drupal.org/node/1089656 and https://www.drupal.org/node/223440#custom-suggestions. 

If you would like a region to NOT show up on the front page, you can simply do not supply content to it and Drupal will not render it. 

If you would like to add an extra region, then google for some tutorials on how to create custom regions. 

Install Devel related modules. 

devel_themer module, make it very easy to do themeing in Drupal, specially if you are new. 

If you have devel_themer installed and enabled, then you can click on the page and see which template file is being used to render the page. You can click on regions, blocks and elements and it will give you details on how it is rendered and which template/function being used. 

Hope this general answer help you.