I added to my header Social media icons and google translator widget, for both of them I used the custom HTML widget, and later design it with the additional CSS.
My question is how can make it appear inside the menu?
you can use this Snippet to hook content inside the navigation and then style it with CSS to suit:
add_action( 'generate_inside_navigation','generate_insert_into_navigation' );
function generate_insert_into_navigation()
{ ?>
Put your HTML or whatever in here
<?php }
Hooks are fine for adding content to be directly displayed in that position but not for adding actions. I would recommend the Code Snippets plugin, it’s used by a lot of the GP community.