How to display additional fileds I've added to a page - the way I want them?
Hiding additional fields is easy, just notice Display Fields tab at the Manage Fields page for the specified content type (page in this case). There you can easily exclude additional fields from being automatically appended to the $content.

In order to show fields the way you want them use themename_preprocess_page hook and check $vars['node'] object for the particular fields.