Need some expert advise/help on an filtered blog post code !!

I have an issue with a filtered blog post page where I would like to show in the filtered menu certain category id’s but where underneath all the posts should be shown. The code where I have to look is this one (according to the designer of the theme, who does not know the answer to my question). The website I am working on can be seen here:
http://bit.ly/17tFLME

The issue is … it is for a news site where there are many categories but I only want some of them to be shown in the filtered menu but all posts underneath in the grid layout. Difficult? Not posible?

<?php

$title = $grid_columns_count = $grid_teasers_count = $grid_layout = '';
$grid_template = $grid_thumb_size = $grid_posttypes = $grid_layout_mode = $grid_taxomonies = $grid_categories = '';
$width = $orderby = $order = $isotope_item = $carousel='';

extract(shortcode_atts(array(
    'title' => '',
    'grid_columns_count' => 4,
    'grid_teasers_count' => 8,
    'grid_layout' => 'thumbnail_caption',
    'grid_template' => 'grid', //grid, carousel
    'grid_thumb_size' => 'blog',
    'grid_posttypes' => '',
    'grid_taxomonies' => '',
    'grid_categories' => '',
	'grid_excerpt_length' => '',
    'grid_layout_mode' => 'fitRows',
    'width' => '1/1',
    'orderby' => NULL,
    'order' => 'DESC',
	'meta_info_large' => ''
), $atts));

if ( $grid_template == 'grid' || $grid_template == 'filtered_grid') {
    wp_enqueue_style('isotope-css');
    wp_enqueue_script( 'isotope' );
    $isotope_item = 'isotope-item ';
} else if ( $grid_template == 'carousel' ) {
    $isotope_item = '';
}

$output = '';

$width = '';
$li_span_class = wpb_translateColumnsCountToSpanClass( $grid_columns_count );

$query_args = array();

// Post teasers count
if ( $grid_teasers_count != '' && !is_numeric($grid_teasers_count) ) $grid_teasers_count = -1;
if ( $grid_teasers_count != '' && is_numeric($grid_teasers_count) ) $query_args['posts_per_page'] = $grid_teasers_count;

// Post types
$pt = array();
if ( $grid_posttypes != '' ) {
    $grid_posttypes = explode(",", $grid_posttypes);
    foreach ( $grid_posttypes as $post_type ) {
        array_push($pt, $post_type);
    }
    $query_args['post_type'] = $pt;
}

// Taxonomies

$taxonomies = array();
if ( $grid_taxomonies != '' ) {
    $grid_taxomonies = explode(",", $grid_taxomonies);
    foreach ( $grid_taxomonies as $taxom ) {
        array_push($taxonomies, $taxom);
    }
}

// Narrow by categories
if ( $grid_categories != '' ) {
    $grid_categories = explode(",", $grid_categories);
    $gc = array();
    foreach ( $grid_categories as $grid_cat ) {
        array_push($gc, $grid_cat);
    }
    $gc = implode(",", $gc);
    ////http://snipplr.com/view/17434/wordpress-get-category-slug/
    $query_args['category_name'] = $gc;

    $taxonomies = get_taxonomies('', 'object');
    $query_args['tax_query'] = array('relation' => 'OR');
    foreach ( $taxonomies as $t ) {
        if ( in_array($t->object_type[0], $pt) ) {
            $query_args['tax_query'][] = array(
                'taxonomy' => $t->name,//$t->name,//'portfolio_category',
                'terms' => $grid_categories,
                'field' => 'slug',
            );
        }
    }
}

// Order posts
if ( $orderby != NULL ) {
    $query_args['orderby'] = $orderby;
}
$query_args['order'] = $order;

// Run query
$my_query = new WP_Query($query_args);

$teasers = '';
$teaser_categories = Array();
if($grid_template == 'filtered_grid' && empty($grid_taxomonies)) {
    $taxonomies = get_object_taxonomies(!empty($query_args['post_type']) ? $query_args['post_type'] : get_post_types(array('public' => false, 'name' => 'attachment'), 'names', 'NOT'));
}

$posts_Ids = array();

while ( $my_query->have_posts() ) {

    $link_title_start = $link_image_start = $p_link = $link_image_end = '';

    $my_query->the_post();

    $posts_Ids[] = $my_query->post->ID;

    $categories_css = '';

    if( $grid_template == 'filtered_grid' ) {
        $post_categories = wp_get_object_terms($my_query->post->ID, $taxonomies);

        foreach($post_categories as $cat) {
            if(!in_array($cat->term_id, $teaser_categories)) {
                $teaser_categories[] = $cat->term_id;
            }
            $categories_css .= ' grid-cat-'.$cat->term_id;
        }
    }

    $post_title = the_title("", "", false);
    $post_id = $my_query->post->ID;

    $teaser_post_type = 'posts_grid_teaser_'.$my_query->post->post_type . ' ';

    // Thumbnail logic
	$thumbnail = '';
    if ( in_array($grid_layout, array('thumbnail_caption', 'thumbnail_title_excerpt') ) ) {
        $post_thumbnail = '';
        $post_thumbnail = wpb_getImageBySize(array( 'post_id' => $post_id, 'thumb_size' => $grid_thumb_size ));
        $thumbnail = $post_thumbnail['thumbnail'];
    }

	/* Caption Logic */
	$format='';
	$videoURL = get_post_meta($post_id, 'reedwan_video_url', TRUE);
	if ( 'post' == get_post_type() )
	{
		if(has_post_format('video') && $videoURL){ $format='<a href="'.$videoURL.'" title="'.__('Play Video', 'realnews').'" class="play-video caption-type"><i class="icon-play-1"></i></a>';}
		else if(has_post_format('audio') && $size='big' && $size!='small'){$format='<a class="caption-type" href="'.get_permalink( get_the_ID() ).'" title="'.__('Play Music', 'realnews').'"><i class="icon-note-beamed"></i></a>';}
		else{$format='';}
	}
	/* Sticky */
	$sticky='';
	if ( is_sticky()){$sticky='<a href="'.get_permalink( get_the_ID() ).'" title="'.__('Featured Post','realnews').'" class="sticky-post"><i class="icon-star"></i></a>';}

	/* Excerpt */
	$excerpt ='';
	if($grid_excerpt_length!='' || $grid_excerpt_length!=0 && $grid_layout == 'thumbnail_title_excerpt')
	{
		$excerpt = '<p>'.string_limit_words(get_the_excerpt(),$grid_excerpt_length).'</p>';
	}

	/* Meta */
	$meta ='';
	if($meta_info_large==true)
	{
		$meta .= '<div class="detailmeta">';
		$meta .= '<span class="time"><i class="icon-clock"></i>'.get_the_time('F j, Y').'</span>';
		$meta .= taqyeem_get_score_alternate(get_the_ID(), 'small');
		$meta .= '</div>';
	}

	/* Caption */
	$caption='';
	if ( $grid_layout == 'thumbnail_caption' ){
		$caption = '<div class="hover-caption-thumb"><a href="'.get_permalink( get_the_ID() ).'" class="caption-link" title="'.the_title_attribute( 'echo=0' ).'">'.the_title_attribute( 'echo=0' ).'</a></div>';
	}

	$link_image_start = $link_title_start = '<a class="link_title" href="'.get_permalink($post_id).'" title="'.sprintf( esc_attr__( 'Permalink to %s', 'js_composer' ), the_title_attribute( 'echo=0' ) ).'">';
    $link_title_end = $link_image_end = '</a>';
	$teasers .= '<li class="builder_grid '.$isotope_item.apply_filters(VC_SHORTCODE_CUSTOM_CSS_FILTER_TAG, $li_span_class, 'vc_teaser_grid_li').$categories_css.'">';

    // If grid layout is: Thumbnail + Captions
    if ( $grid_layout == 'thumbnail_caption' ) {
        if ( $thumbnail ) {
			$to_filter = '<div class="mediaholder">' .$format . $sticky .'<a href="'.get_permalink($post_id).'">'.$thumbnail . '</a>'. $caption .'</div>';
            $teasers .= apply_filters('vc_teaser_grid_thumbnail', $to_filter, array("grid_layout" => $grid_layout, "ID" => $post_id, "thumbnail" => $thumbnail) );
        }
    }
	// If grid layout is: Thumbnail + Title + Excerpt
    if ( $grid_layout == 'thumbnail_title_excerpt' ) {
        if ( $thumbnail ) {
            $to_filter = '<div class="mediaholder">' .$format . $sticky.'<a href="'.get_permalink($post_id).'">' . $thumbnail . '</a></div>';
            $teasers .= apply_filters('vc_teaser_grid_thumbnail', $to_filter, array("grid_layout" => $grid_layout, "ID" => $post_id, "thumbnail" => $thumbnail) );
        }
        if ( $post_title ) 	{
            $to_filter = '<div class="detailholder"><h4>' . $link_title_start . $post_title . $link_title_end . '</h4>'.$excerpt.$meta.'</div>';
            $teasers .= apply_filters('vc_teaser_grid_title', $to_filter, array("grid_layout" => $grid_layout, "ID" => $post_id, "title" => $post_title) );
        }
    }

    $teasers .= '</li> ' . $this->endBlockComment('single teaser');
} // endwhile loop
wp_reset_query();

if( $grid_template == 'filtered_grid' && $teasers && !empty($teaser_categories)) {

    $categories_array = get_terms($taxonomies, array(
        'orderby' => 'name',
        'include' => implode(',', $teaser_categories)
    ));

    $categories_list_output = '<ul class="categories_filter clearfix">';
    $categories_list_output .= '<li class="active"><a href="#" data-filter="*">' . __('All', 'js_composer') . '</a></li>';
    foreach($categories_array as $cat) {
        $categories_list_output .= '<li><a href="#" data-filter=".grid-cat-'.$cat->term_id.'">' . esc_attr($cat->name) . '</a></li>';
    }
    $categories_list_output.= '</ul><div class="clearfix"></div>';
} else {
    $categories_list_output = '';
}

if ( $teasers ) {
	if ( $grid_template == 'carousel' ) {
		$carousel = apply_filters( 'vc_teaser_grid_carousel_arrows', '<div class="carousel-nav"><a href="#" class="prev icon-left-open-big"></a> <a href="#" class="next icon-right-open-big"></a></div>' );
	}
	$teasers = '<div class="teaser_grid_container">'.$categories_list_output. $carousel.'<ul class="wpb_thumbnails wpb_thumbnails-fluid clearfix" data-layout-mode="'.$grid_layout_mode.'">'. $teasers .'</ul></div>';
}
else {
	$teasers = __("Nothing found." , "js_composer");
}

$posttypes_teasers = '';

if ( is_array($grid_posttypes) ) {
    $posttypes_teasers_ar = $grid_posttypes;
    foreach ( $posttypes_teasers_ar as $post_type ) {
        $posttypes_teasers .= 'wpb_teaser_grid_'.$post_type . ' ';
    }
}

$grid_class = 'wpb_'.$grid_template . ' columns_count_'.$grid_columns_count . ' grid_layout-'.$grid_layout . ' '  . $grid_layout.'_'.$li_span_class . ' ' . 'columns_count_'.$grid_columns_count.'_'.$grid_layout . ' ' . $posttypes_teasers;
$css_class =  apply_filters(VC_SHORTCODE_CUSTOM_CSS_FILTER_TAG, 'wpb_teaser_grid wpb_content_element '.$grid_class.$width, $this->settings['base']);

$output .= "\n\t".'<div class="'.$css_class.' block clearfix">';
$output .= "\n\t\t".'<div class="wpb_wrapper">';
$output .= wpb_widget_title(array('title' => $title, 'extraclass' => 'wpb_teaser_grid_heading'));
$output .= $teasers;
$output .= "\n\t\t".'</div> '.$this->endBlockComment('.wpb_wrapper');
$output .= "\n\t".'</div> '.$this->endBlockComment('.wpb_teaser_grid');

echo $output;

I am not sure where to look and what to place, if all posible. Personally I also think this next code is in need of change but still, no sure what to put here and if it is posible to do such a thing.

<?php
/**
 * Create filter
 * {{
 */
if( $filter === 'yes' && !empty($this->filter_categories)):
    $categories_array = $this->getFilterCategories();
?>
    <ul class="categories_filter clearfix">
        <li class="active"><a href="#" data-filter="*"><?php _e('All', 'js_composer') ?></a></li>
    <?php foreach($this->getFilterCategories() as $cat): ?>
        <li><a href="#" data-filter=".grid-cat-<?php echo $cat->term_id ?>"><?php echo esc_attr($cat->name) ?></a></li>
    <?php endforeach; ?>
    </ul><div class="clearfix"></div>
<?php endif; ?>

I am sort of a newbie but eager to learn but in need of some help.
Thanks anyone. Regards, Remco