We are planning to use RMAN/TDP(Tivoli Data Protector) for backups for our new project.I would like to know what would be the best strategy for this.What we are planning is:

1.A closed RMAN full backup on weekends(We are allowed to shutdown the database on weekends).
2.An incremental RMAN backup on weekdays.

Now the question is I don't know whether we can have incremental backups with CLOSED full backups.If this is possible then I guess our current stratergy should be OK,otherwise we have to do an OPEN full backup as well.

The bigger problem is managing archive logs.We want to keep the backups of archive logs for a minimum of 7 days and after that automatically delete the previous logs from the diskand tapo.Is it advisable to do this from a Unix script or use RMAN to do everything.What would be the best way to do it.Any suggestions/scripts would be welcome.