add a menu item to wp menu

How would I add a menu item to my wp menu with a function in my theme’s function.php? I’ve found the following snippet online which works but not to exactly how I want it.

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The function above uses wp_login_url & wp_logout_url. I’ve created a custom login page which I want to use, how can I edit the code above to use the custom page (page_id=#) instead and redirect to a (page_id=#) after successful login? Also how can I add a class to the function to style the menu link? Thanks!