Looking for subpage and subcategory template

If I’m understanding you, the WordPress Default Theme will do most of that, and this change should handle the rest–

For use in sidebar, display only top level Pages, but when viewing a Page that has children (or is a child) show only children of that parent
When visiting main page, all top level pages are listed in the sidebar.
When click on a top level page with no children, all top level pages are listed.
When click on a top level page with children, just the children pages are listed.
When click on a children page, just the children of that parent are listed.

<?php
$output = wp_list_pages('echo=0&depth=1&title_li=<h2>Top Level Pages </h2>' );
if (is_page( )) {
  $page = get_query_var('page_id');
  if ($post->post_parent) {
    $page = $post->post_parent;
  }
  $children=wp_list_pages( 'echo=0&child_of=' . $page . '&title_li=' );
  if ($children) {
    $output = wp_list_pages ('echo=0&child_of=' . $page . '&title_li=<h2>Child Pages</h2>');
  }
}
echo $output;
?>