Filter In Reply comments from WordPress Admin Panel

In your comments loop, skip the children:

if( !empty( $comment->comment_parent ) ) { 
    //if the comment has a parent, skip it as it's not level 1
    continue;
}

Edit: Above example would only help in the reading loop, below example should help in admin area:

add_filter('the_comments', 'top_level_comments_filter');

function top_level_comments_filter($comments){
    global $pagenow;
    if($pagenow == 'edit-comments.php'){
        foreach($comments as $key => $value){
            if( !empty( $value->comment_parent ) ) { 
                unset($comments[$key]);
                continue;
            }
        }
    }
    return $comments;
}

Edit: Per your addendum to the original question, this would be how you put it all together. I’ve cleaned up your code a little and given the functions a cohesive name-space. This lumps the filter I gave you in with the condition of the ask query var being set:

add_action( 'current_screen', 'dreis_comments_exclude_lazy_hook', 10, 2 );

/**
 * Delay hooking our clauses filter to ensure it's only applied when needed.
 */
function dreis_comments_exclude_lazy_hook( $screen ) {
    if ( $screen->id != 'edit-comments' ) {
        return;
    }

    // Check if our Query Var is defined    
    if( isset( $_GET['ask'] ) ) {
        add_action( 'pre_get_comments', 'dreis_list_comments_from_specific_post', 10, 1 );
        add_filter( 'the_comments', 'dreis_top_level_comments_filter' );
    }

    add_filter( 'comment_status_links', 'dreis_new_comments_page_link' );
}

/**
 * Only display comments of specific post_id
 */ 
function dreis_list_comments_from_specific_post( $clauses ) {
    $clauses->query_vars['post_id'] = 12;
}

/**
 * Add link to specific post comments with counter
 */
function dreis_new_comments_page_link( $status_links ) {
    $count = get_comments( 'post_id=12&count=1' );

    if( isset( $_GET['ask'] ) ) {
        $status_links['all'] = 'All';
        $status_links['ask'] = 'Ask ('.$count.')';
    } else {
        $status_links['ask'] = 'Ask ('.$count.')';
    }

    return $status_links;
}

/**
 * Remove non-top-level comments
 */
function dreis_top_level_comments_filter($comments){
    global $pagenow;
    if($pagenow == 'edit-comments.php'){
        foreach($comments as $key => $value){
            if( !empty( $value->comment_parent ) ) { 
                unset($comments[$key]);
            continue;
            }
        }
    }
    return $comments;
}