Im trying to access the Magento customer session in another part of my website.
domain.com/shop/ <- Magento
domain.com/test.php
The shop
I would recommend checking the path of the cookie that Magento sets. Most likely, it is set to /shop, so the cookie will not be accessible to your file above it.
You can modify the path that Magento uses to set its cookie in the control panel under System -> Configuration -> Web (under the General heading) -> Session cookie management