No no no! Never POST or link directly to a custom PHP file – WordPress won’t be loaded, and to load it manually yourself means making huge assumptions about the file hierarchy.
Use the ajax API, which exists specifically for this reason:
$.ajax({
url: "<?php echo esc_js( admin_url( 'admin-ajax.php' ) ) ?>",
type: "POST",
data: {
action: "update_button",
button: $( this ).val()
}
});
And for your PHP:
function wpse_227396_update_button() {
switch ( filter_input( INPUT_POST, 'button' ) ) {
case 'Save News':
add_content(303);
break;
case 'Save About Us':
add_content(75);
break;
case 'Save Contact':
add_content(30);
break;
}
}
add_action( 'wp_ajax_nopriv_update_button', 'wpse_227396_update_button' );
add_action( 'wp_ajax_update_button', 'wpse_227396_update_button' );