What you want is very simple but also takes a lot of work to make it work as you expected.
The first start will be to create a base page. This page will be responsible for all of the requests.
For example :
idontripmoviesandseries.com/videogalerie/show1/season1-episode1/
Now you want to tell WP how to handle this kind of urls
https://developer.wordpress.org/reference/functions/add_rewrite_rule/
example code
add_rewrite_rule(
'^videogalerie/[^/]+)/([^/]+)?$',
'index.php?pagename=videogalerie&showname=$matches[1]&episodeseason=$matches[2]',
'top'
);
But somehow you need to tell WP to understand these new parameters (showname and episodeseason )
add_filter( 'query_vars', 'set_videogalerie_query_vars' );
function set_videogalerie_query_vars( $vars ) {
$vars[] = 'showname';
$vars[] = 'episodeseason';
return $vars;
}
Now you can do what you want on the template of the videogalerie page.
You can make a request to the third party API retrieve the data you want and parse them before loading the page.
The Ajax part not sure why you need it as this way the server can load the full list of url Shows and Seasons before showing to the user. But if you want that this can be handled by this answer wordpress.stackexchange.com
Have fun!