Custom CSS File wont work on second Page

Sounds like your are not creating a proper WordPress template when you copy your index.php.

Here you can find the list of standard template files: https://codex.wordpress.org/Theme_Development#id=%22Template_Files_List%22

And here you can learn how to create a custom template:
https://codex.wordpress.org/Theme_Development#Custom_Page_Templates

My guess is you need to add the following to the top of your index copy. Then make sure to select this template from the edit post/page view to use it on the front end (it should use the css).

<?php
/*
Template Name: Index Copy
*/