Fatal error: Uncaught Error: Call to undefined function wp_nav_menu()

Yes, like @fuxia says, include wp-load.php to get the WordPress API (wp_nav_menu included) to use. In your case:

<?php

include '../../../../wp-load.php';

This way you did is not wrong but there are better ways to use AJAX in WordPress:

https://codex.wordpress.org/AJAX_in_Plugins

Be happy, my friend!

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