Syntax error

[GustavoIglesias]

On the function "parse_query", where you writes:
if ( $cat_id = $cat->term_id )
¿Must be?
if ( $cat_id == $cat->term_id )
It's an error: you assig in a comparison.
By the way, you must inicialize the $cat_id variable; In the code above
if(isset($q->query_vars['cat']) && !empty($q->query_vars['cat'])){
$cat_array = array_map('intval', array_map('trim', explode(',', $q->query_vars['cat'])));
}
You MUST put an ELSE to