I’m not sure if select multiple value from the select box is what you want, but from a quick look at you code i would say you should put
<select name="'.$field['id'].'[]" id="'.$field['id'].'">
instead of
<select name="'.$field['id'].'" id="'.$field['id'].'">
since you want a multiple select. This is then a html problem, not a WP related.