How to retrieve media images urls in different sizes?

Question

I don’t understand your code in full (how your foreach’s actually fill your list item), but, as for the specific question, I think that the function you want is wp_get_attachment_image_src();

So (illustratively):

   $thumbnail_src = wp_get_attachment_image_src( $picture->ID );
   $image->thumbnail_url = $thumbnail_src[0];
   $full_src = wp_get_attachment_image_src( $picture->ID, 'full' );
   $image->full_url = $full_src[0];