How can I fetch the next level of the currently selected main menu (hierarchical menu)?

You can accomplish this in at least two ways:

1) Via CSS. Use the appropriate class selectors (e.g. current-page-item, current-page-parent, current-page-ancestor) to display the appropriate sub-menu.

2) Separate calls to wp_list_pages(). The first call will have a depth=1 argument passed, and the second will determine the ID of the current parent page, and output accordingly, using the “child_of” argument, e.g.:

<?php
global $post;
$current_page_parent = ( $post->post_parent ? $post->post_parent : $post->ID );

wp_list_pages( array(
     'title_li' => '',
     'child_of' => $current_page_parent,
     'depth' => '1' )
);
?>

There are probably other ways, as well.