Custom taxonomy page template name and how to use it?

where it should be placed whether in page-template directory or at theme root directory?

It should be placed at the root directory of the the active theme.

If you take a look at template heirarchy, you can see that for taxonomy the flow is:

taxonomy-$taxonomy-$term.php --> taxonomy-$taxonomy.php --> taxonomy.php

So the correct name for term (Asia) is taxonomy-location_category-asia.php instead of taxonomy-asia.php and the same for other terms also.