In a Data Guard environment, offloading backups to a physical standby database has certain requirements:

A: Once the primary database is registered in an RMAN catalog, the standby database can also be registered. This allows RMAN to manage backups coherently across both databases and leverage the standby database for backup purposes without interfering with the primary database's workload.

C: Backups of the standby control file taken while connected to the catalog where the database is registered can be used to restore the control file on the primary database. This ensures that backup metadata is consistent across the Data Guard configuration.

Options B and D are incorrect because there is no strict requirement for the order in which the primary and standby databases must be registered in an RMAN catalog. However, it is a common practice to register the primary database first.