*1) How i can restore a media backup which has been taken from Primary (DC) to another (DR) server?*
-- Assuming each location has a different OSB catalog. Import the volume, then backup metadata into OSB catalog then you should be able to restore in alternate domain:
Reads each backup image label on each volume. You can use this option if you are importing volumes from another administrative domain. This option requires specification of a tape drive. This option imports information regarding the tape into volumes and archive catalogs. To import backup metadata stored in the tape, use --obtaropt with the -G option.
Example B-16 Cataloging a File-System Backup Image
Example B-17 Cataloging an RMAN Backup Image
2) How to assign a media to a particular media family ?
--- You can prelabel tapes, but why do you want to? When a backup operation is kicked off, OSB automatically chooses a tape of same media family or if unlabeled tape is used...OSB automatically labels it with appropriate media family
3) How to restore a data from an expired media?
--- If tape has not been overwritten, then OSB still has information about the tape and will restore from it as usual.
4) How to manually expire a media for reuse?
--- force unlabel the tape : http://docs.oracle.com/cd/E26569_01/doc.104/e21480/obtool_commands.htm#autoId150