register_taxonomies and standard post types

I am trying to add some taxonomies. Everything works as expected with my own custom post types, but it is not working as I expect (or hope!) with standard post types.

(1) I can add a new taxonomy to pages, and the taxonomy shows up fine when I create/edit a post. However, I do not get a link to edit that taxonomy’s terms in the ‘Page’ section of the admin menu – i.e. a link to wp-admin/edit-tags.php?taxonomy=my_new_taxonomy. If I attach the taxonomy to both pages and posts, the edit menu is added as expected to the ‘Posts’ section, but it never gets added to ‘Pages’. Is this a bug, or am I missing something? I am adding the taxonomy using:-

register_taxonomy('my_new_taxonomy',array('page','post'),array(
    'hierarchical' 	=> TRUE,
    'label' 		=> 'New Taxonomy',
    'singular_label'	=> 'New Taxonomy',
    'public' 		=> TRUE,
    'show_ui' 		=> TRUE,
    'rewrite' 		=> FALSE
  ));

(2) I would like to add a category taxonomy to images, and a hierarchical category taxonomy to links. Is this possible? Using the above code but with post types ‘link’ and ‘attachment’ doesn’t add anything in the admin interface for links/media.

Thanks,

mark.