Hello,
If you set the policy trigger to login, it will run as the current user. You can also set a module to use an impersonation account where the system account will run the installation as that user, but that's meant more for applications that won't install with system, you would probably use just a single impersonation account.
The custom attributes cannot be used in the client scripts, currently they can only be used in imaging scripts, but I can add this to the next release.
You can use a custom inventory script to collect the information from your powershell script which can be used in reports but cannot be passed to a script.