There are more issues in this regard than you realize. First of all, you shouldn’t directly request custom PHP files in WP. There is no reliable way to invoke the WP environment when you do this. If you are utilizing shortcodes to cause your custom code to execute, there is no reason for a separate file. Put the shortcode in a post and make the request using the post’s permalink. You may add URL parameters like you would any other URL.
Besides using shortcodes, there are 4 other valid ways in WP to cause custom code to execute. 1) hook a filter or action. 2) Use Ajax. 3) Make a custom page template. 4) send your request through wp-admin/admin-post.php.
Don’t bother with Insert PHP plugin. If you can write PHP within the shortcode, you can just as easily create your own shortcode without the plugin. There is also some added security risk in using Insert PHP and similar plugins. The way the plugin works might also be why you are having trouble with getting URL parameters, but I cannot be sure about this.
The main thing to remember in making your own shortcode is the handler function must never generate output by using echo, fprint, etc. Instead, accumulate output into a variable that your handler function returns. WP will then echo out the returned string at the appropriate location in the post.
