Search in Archive Pages by subcategory, tag, custom field and year

You only need one form and a callback on pre_get_posts. For example:

<form role="search" method="get" id="searchform" action="<?php echo $current_url; ?>">
    <input type="hidden" name="s" value="true" />

    <!-- Tag Search -->
    <label for="tags">Search Tag:</label>
    <input type="text" value="Search" name="tags" id="tagsearchbox" />

    <!-- Custom Field "autor" Search -->
    <label for="autors">Search in Custom Field 'autor':</label>
    <input type="text" value="Search" name="autors" id="autorsearchbox" />

    <input id="searchsubmit" value="Search" type="submit">
</form>

Now your callback:

function alter_search_ppp_wpse_107154($qry) {
  if ($qry_>is_main_query() && $qry->is_search()) {
    // parse your fields here and alter the query with $qry->set like this :
    $qry->set('post_per_page',10);
  }
}
add_action('pre_get_posts','alter_search_ppp_wpse_107154');

You should validate that code. You have strange things happening, like multiple id attributes on some elements and put that Javascript in a file and enqueue it.