pull data from a remote wordpress database

Ok. There are few things wrong here.

query_posts isn’t mean to be used that way so don’t. Try the same code with $likes=new WP_Query(array(... instead.

$likes=new WP_Query(array(
                        'post_type' => 'post',
                        'ignore_sticky_posts' => true,
                        'filter_type' => 'user_liked',
                        'filter_user' => $user_id
                    ));

That is problem one. Then even if $likes were set correctly you’d clobber it.

$likes= array();

Why would you expect to have data in $likes after you’ve erased all of the data? Don’t do that. Remove that line.

Now this:

while (have_posts()) : 
    $likes[]=the_post() ;
endwhile;

…is pointless. After you run the query $likes is already a collection of posts. Run var_dump($likes) and you will see what I mean. There is no need to loop over it just to do what is already been done. Just return $likes or loop over it and do something, like echo content.

Besides, using the_post like that wouldn’t work. That isn’t what the the_posts method does.

If, on the other hand, you are trying to extract, for example, the post content you’d want…

while ($likes->have_posts()) : 
    $likes->the_post();
    $cont[] = $post->post_content;
endwhile;

I’d really suggest you take some time to read about creating loops.

You can do about the same with get_posts but the loops are a little different.

Also, why are you mixing PHP’s mysql_* functions with $wpdb? And why are you using global $wpdb only to then clobber it? Why don’t you just use a different name for your database instance?

Hopefully that helps.