Link to subpages on the same page

get_children is the most straightforward way to get “attachments, revisions, or sub-Pages”. So…

$children = get_children(array('post_parent'=>$post->ID));
if (!empty($children)) {
  foreach ($children as $child) {
    echo '<div id="child-'.$child->ID.'" >';
      // content formatted however you want
    echo '</div>';
}

See the Codex page for further parameters that you might need.

I don’t know how you’ve constructed your drop-down menu but you can link to any element on the page using its id attribute so your href for the links should be #child-<ID>, preferably constructed as an absolute URL.