Ajax doesn't load seperate PHP file

Hi,
I setup a custom template for one page, because we need some kind of configurator which gets data from database.
I have three files:
1. Template for wordpress (I copied the page.php for the child theme)
2. configuration.php
3. load_data.php

The configuration.php is included in the template.
At the end of the configuration.php I load the data.php by ajax for the query of what is selected and what should be shown.

My code works, because when I run it at my localhost everything is fine. I think its the ajax part, which cannot load the right way to call the load_data.php.
I also tried to add the script in the functions.php to load it in the footer (and I also replaced $ with jQuery) – didn’t work

Code configuration.php:
https://pastebin.com/AUF2XetV

Code load_data.php:
https://pastebin.com/XVYtBzBv

ajax should load in the footer of the configuration.php, but that couldn’t work, because the footer is loaded seperatly. I also tried to adjust the footer.php for my child-theme. But that doesn’t work either.
This is the ajax code to call the load_data.php:

<script>
 $(document).ready(function(){
      $('#brand').change(function(){
           var brand_id = $(this).val();
           $.ajax({
                url:"load_data.php",
                method:"POST",
                data:{brand_id:brand_id},
                success:function(data){
                     $('#show_model').html(data);
                }
           });
      });
 });
 </script>

I also tried to add this snippet in the functions.php (also replaced $ with jQuery) but my selection doesn’t work.

Since it works on my localhost the problem has to be the position of the ajax script.
I am not a developer and I spent a lot of time to make this work :), so please keep answers as simple as possible to understand :). I just need to find a workaround.

Dropbox download for video snippets (screen records):
https://www.dropbox.com/sh/702tjj78gkm9xeg/AABrQVvEXTCFAKueCCmB545-a?dl=0
(design hasn’t been made yet)

localhost.mp4 = how it should work
internal_testserver_wordpress.mp4 = how it (doesn’t) work in wordpress

Kind regards,
Lucas