The following code removes the Customizer links, Background and Header from the Toolbar drop-downs:

/**
 * Remove Customize menus from the Toolbar.
 *
 * @param WP_Admin_Bar $wp_admin_bar WP_Admin_Bar instance.
 */ 
function wpdocs_remove_customize( $wp_admin_bar ) {
	// Remove customize, background and header from the menu bar.	
	$wp_admin_bar->remove_node( 'customize' );  
	$wp_admin_bar->remove_node( 'customize-background' );   
	$wp_admin_bar->remove_node( 'customize-header' );   
}
add_action( 'admin_bar_menu', 'wpdocs_remove_customize', 999 );

The following code removes the WP logo and the Comments menu:

/**
 * Remove WP logo and comments from the Toolbar.
 *
 * @param WP_Admin_Bar $wp_admin_bar WP_Admin Bar instance.
 */
function wpdocs_remove_logo_comments( $wp_admin_bar ) {
	// Remove wp-logo and comments from the menu bar.
	$wp_admin_bar->remove_node( 'wp-logo' );  
	$wp_admin_bar->remove_node( 'comments' );    
}
add_action( 'admin_bar_menu', 'wpdocs_remove_logo_comments', 999 );