As the question was modified, I modify my answer. This task is relatively easy, doable just with a single rewrite rule, which converts everything after /mypage/ string into a variable – I call it var. As this is added to query_vars via hook, is reachable via global $wp_query; echo $wp_query->var;
.
add_filter( 'query_vars', 'binda_query_vars' );
function binda_query_vars( $vars ) {
$vars[] = 'var';
return $vars;
}
add_action( 'generate_rewrite_rules', 'binda_rewrite_rules' );
function binda_rewrite_rules( $wp_rewrite ) {
$mypage_id = 4; //setup your 'mypage' ID
$wp_rewrite->rules = array(
'mypage/(.+?)/?$' => $wp_rewrite->index . '?page_id='.$mypage_id.'&var=" . $wp_rewrite->preg_index( 1 ),
) + $wp_rewrite->rules;
}