How do I override menu items with my own implementation?
You can use hook_menu_alter() to reroute the request for that page to your own module's functions:

function MYMODULE_menu_alter(&amp;$items) {
  $items['user/%user/edit']['access callback'] = 'MYMODULE_access_callback';
  $items['user/%user/edit']['page callback'] = 'MYMODULE_user_edit_page_callback';
}

function MYMODULE_access_callback($account) {
  if ($something) {
    return FALSE;
  }

  return TRUE;
}

function MYMODULE_user_edit_page_callback($account) {
  if ($something) {
    return drupal_get_form('some_form');
  }
  else {
    return drupal_get_form('some_other_form');
  }
}