How do I integrate a nodes edit form on a page?
Use drupal_get_form(NODETYPE . '_node_form', NODEOBJECT); as callback in your custom menu item.
The original node module callback for menu item 'node/%node/edit' is located in the node.pages.inc file:

/**
 * Menu callback; presents the node editing form.
 */
function node_page_edit($node) {
  $type_name = node_type_get_name($node);
  drupal_set_title(t('&lt;em&gt;Edit @type&lt;/em&gt; @title', array('@type' =&gt; $type_name, '@title' =&gt; $node-&gt;title)), PASS_THROUGH);
  return drupal_get_form($node-&gt;type . '_node_form', $node);
}