Pass GET params to URL from a main menu item

The 404 issue is because name is a WordPress query var. Adding that in the URL causes WordPress to query for a post with slug that matches whatever is in the name field, instead of your page. Change your form field names to something you know will be unique. This is a good practice for everything you have to name- form fields, functions, etc..

As for your menu item question, you can use the nav_menu_link_attributes filter to alter the href for a specific menu item. Here we check if Trainings is the title of the menu item, and add the GET params if that is the case:

function wpd_add_logged_in_get_params(){
    if( is_user_logged_in() ){
        add_filter( 'nav_menu_link_attributes', function( $atts, $item ){
            if( 'Trainings' == $item->title ){
                $current_user = wp_get_current_user();
                $atts['href'] = esc_url(
                    add_query_arg(
                        array( 
                            'wpd_name' => $current_user->display_name,
                            'wpd_email' => $current_user->user_email
                        ),
                        $atts['href']
                    )
                );
            }
            return $atts;
        }, 10, 2 );
    }
}
add_action( 'template_redirect', 'wpd_add_logged_in_get_params' );