how do I delete (not exclude) a menu item from navigation bar

I’m building a site’s navigation bar programmatically, using the following code:

wp_update_nav_menu_item($menu->term_id, 0, array(
    'menu-item-title' =>  $page_data->post_title,
    'menu-item-classes' => 'main',
    'menu-item-url' => '/', 
    'menu-item-status' => 'publish'));

this adds menu items to my navigation bar and works well. I use this to pre-populate a number of menu items when site is created.

The question is how do I delete a menu item from the nav menu? (for example if user wants different menu items in the nav bar).
I know that I can use exclude, but that doesn’t seem like the right solution since I don’t want to constantly manage the exclude list based on user changes.

another question: how do I change menu order via code?

thanks!

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