How to add Search form/Advanced search form view to advanced forum pages?
You need to display the exposed filters in a block, and then display that block on single forum node pages.

Here's how to do that:


Edit the Forum Search view: /admin/structure/views/view/advanced_forum_search/edit.
Under "Exposed form" -> "Exposed form in block" choose "Yes".
Save the view.
Navigate to /admin/structure/block.
Enable the "Exposed form: advanced_forum_search-page" block, and show it for example in the "Content" area and only for "Forum topic" nodes. You can change this to your liking of course.


Users now can use this form from single forum nodes, and submitting it will take them to the search page.

Update

If you want to make this available in your templates and position it within other elements, you'll have to edit the template.php of your theme add a hook_preprocess_X() implementation.

Choice depends on the template you want to add the form to. For example:


hook_preprocess_node() - to make the form available in node.tpl.php
hook_preprocess_page() - to make the form available in page.tpl.php
hook_preprocess_html() - to make the form available in html.tpl.php


Here's the code:

function YOUR_THEME_preprocess_REPLACE_THIS(&amp;$variables) {
  // Load the view and generate the search form.
  //
  // You can have any dynamic conditions here (e.g. limit to some content types
  // and so on).
  $view = views_get_view('advanced_forum_search');
  $view-&gt;set_display('page');
  $view-&gt;init_handlers();
  $form_state = array(
    'view' =&gt; $view,
    'display' =&gt; $view-&gt;display_handler-&gt;display,
    'exposed_form_plugin' =&gt; $view-&gt;display_handler-&gt;get_plugin('exposed_form'),
    'method' =&gt; 'get',
    'rerender' =&gt; TRUE,
    'no_redirect' =&gt; TRUE,
  );
  $variables['search_form'] = drupal_build_form('views_exposed_form', $form_state);
}


Then in your .tpl.php file you would use this code to display the form:

&lt;?php print render($search_form); ?&gt;


Note that this way the visibility settings in admin won't be applied.