Is the boxed version of Battlefield 3 free from other clients, "services", and DRM? For instance, the intrusive "always online" DRM, "3-install" limits, Origin, and so on.
No. Origin is required for any PC copy (boxed and digital) of Battlefield 3.
Origin is required to play at all times (you can use the offline mode though).
You must also pass a one time release date check the first time you use Battlefield 3, which requires the internet. After that you're free to play offline (but still through Origin).