Adding $id variable to custom link in nav menu

The text you put into the menu entries is expected to be HTML and CSS, it will not be examined for PHP variables. What you need to do is to register a filter function, inside the filter function you get to replace a piece of text with the id number.
List of filters here:
http://adambrown.info/p/wp_hooks/hook/filters
It is hard to know just which one to pick, this can require experimentation and reading theme and core code. To my eye’s this one looks like a good candidate: wp_nav_menu
So I would put this code into my (child) theme’s functions.php file:

// filter user ID into menu links
function custom_filter_menu_UserID( $args ) {
	$id = '';
	if( is_user_logged_in() ) $id .= wp_get_current_user()->ID;
	return str_replace('UserId_HERE', $id, $args);
}
add_filter( 'wp_nav_menu', 'custom_filter_menu_UserID' );

And put this into your menu:
http://www.mywebsite.com/?page=portrait&id=UserId_HERE

Glad it worked.
Just had a thought, what happens if someone just starts to add numbers at random to the url, like this:
http://www.mywebsite.com/?page=portrait&id=1234
They get to view any user’s page they have the patience to find.

If you want people to only view their own pages, then:
Give the “page=portrait” page a custom page template in your theme, using PHP code in the template set the $id to that of the logged in user, fakery is no longer possible. Of course you also test if the user is logged in, if not display “You must be logged in to view this page”