No, for the sake of data integrity, after a service date has passed, it cannot be edited.
If you want to recreate the service for another day, you can go to the service and click the link near the bottom to "Make a copy of this service".
You do not need to add hymns and psalms to the service plan in order to utilize Christian Worship: Service Builder's reporting capabilities. Hymn usage is reported when a bulletin or presentation containing the hymn is exported.